I have celiac's disease and have been gluten free for ~8 years, but I'm not super knowledgeable on veganism so here's an info dump that may or may not help.

Have you got any other allergies or dietary restrictions? Lots of gluten replacements in recipes or vegan replacements are nut based, use soy, or involve coconut, or the replacement is nonvegan/nonglutenfree. Make sure you aren't trading a stomach ache for an anaphylactic reaction (my cousin literally almost killed himself eating vegan tacos made with cashews).

You're gonna want to get comfortable with naturally gluten free meals, many of which are also naturally vegan: rice, potato, bean, and chickpea dishes, or veggie based meals like salads, chilis, curries, and soups, or start using veggies to replace the things you cut out (cauliflower wings, lettuce wraps, vegan cheese, spaghetti squash instead of pasta, etc) until you find gluten free versions of stuff you like that are also vegan.

Celiacs like me often replace gluten based staple foods with storebought gluten free versions but those versions aren't necessarily healthier for you (and often aren't vegan); if it's carbs/sugars/artificial ingredients in the glutinous foods that are upsetting your stomach then the gluten free substitutes might actually be a lot worse for you. Consider asking your doctor or having your mom ask hers for a blood test looking at transglutaminase levels (do it before you go gluten free or it wont tell you shit) or ask for an endoscopy to look for damage from gluten intolerance/celiac's disease/crohns/colitis; they can be very similar in effects but how you change your diet to adapt to them is very very different. A lot of the gluten free substitutes off the shelf are both heavy in corn (will make you fatter) and expensive - i think i paid $8cdn for 6 frozen english muffins (had eggs and milk), and like $4-6cdn for frozen bread (one brand was vegan, one had eggs). If you want to make your own breads you will need to research a lot of flour mixes and the upfront costs may be very high while you figure out your preferred method (you will almost certainly want xanthan gum if you won't be adding eggs).

Assuming gluten is the issue, here's a shit load of things I've learned, I err on the side of caution due to celiac's but you might be able to be a bit looser about cross contamination if you haven't got that:

• if a label says 'may contain wheat/made in a factory that processes wheat' treat it as though it says 'contains wheat',
• toasters are never clean no matter how much you scrub them, just get a new one and only use it for gluten free breads, keep it up high so no one spills crumbs or flour near it or accidentally uses it for regular bread
• avoid oats unless specifically labeled gluten free (they are often stored or shipped together and there is always cross contamination),
• avoid anything that says barley, barley malt, or rye as they have gluten, (but weirdly hard liquors are okay for some people as distillation should remove all proteins but unless the bottle is labeled gluten freethere's no guarantee you won't feel sick),
• check your soy sauce bottles as most have wheat for some reason, and most worchestershire sauces have wheat as well,
• be careful of anything that starts with a roue because that's often wheat; make it yourself instead if it isn't labelled gluten free,
• when experimenting with recipes and flour blends keep a log or journal or jot notes on your recipe card; specifically note the flours/flour blends you used and when you try a different one write that down too and write down how you compare it to your initial recipe; fluffier, tastes gritty, crumbles easily, very wet, requires longer to cook, etc. you may also have to do this for butter or egg replacements so a good organized binder of recipes and notes will probably help a lot
• gluten free beer does exist but don't get one like Daura that says 'gluten removed' because that's literally russian roulette of cross-contamination, stick with one made from other grains like rice, sorghum, or millet
• be super extra careful in grocery stores as many places put the vegan, organic, and gluten free items all together in one section: some items may be all three but usually there is a gluten free item that is very not vegan next to a vegan item that is full of wheat next to an organic item that is neither gluten free nor vegan; read the labels very carefully
• avoid eating out/ordering in unless the place is known for their strict policies for allergies (pizza or sub places often have gluten free options but their kitchens are hectic and you can easily get flour somewhere accidentally),
• lots of local places have gluten free chefs, bakers, and owners and are often perfect because they want to be able to eat their own food (these places are not always vegan, but many vegan places understand gluten intolerance and can find you something) i find local thai, vietnamese, and mexican restaurants are the safest
• fast food places like mcdonalds and burger king are generally a bit too risky for me (minimum wage isn't enough to care about cleaning an area to prevent cross-contamination for one order when you're being yelled at to make shit faster, everything gets done in the same places by the same people doing everything else)
• lots of places with smoothies or ice cream or syrups are a trap; having worked in a few, most of their ice creams or sorbets are made in the same factories as their breads and cookies so there's no guarantee any of it is gluten free (they're labelled as may contain wheat on the big buckets but not the up front buckets so most employees never notice it unless they know to look for it/don't realise that may contain means not gluten free)
• if you order anything from a restaurant start by asking them about their gluten free options or specify you want the item gluten free; lots of stuff is only one ingredient away from being safe but if 'gluten free' isn't on the chit it won't be made safely
• check your treats carefully; lots of chips are gluten free but lots aren't, and candies, nuts, and frozen deserts can often be made or packaged in facilities alongside wheat,
• look at your spices; some cheaper store brands are not gluten free, some more expensive spice mixes like steak rub or marinades can be full of gluten
• if you already make your own baked goods like cakes or muffins you will honestly not feel much of a difference with your deserts once you find a mix or brand of gluten free flour you like
• lots of people say you can't make anything good with almond flour or rice flour or bean flour or whatever but its all about what flavours and textures you like and what else goes in your baked goods; we've made pies, pizzas, breads, muffins, cookies, edibles,lasagnas, casseroles, soups, cakes, fried chicken, brownies, lemonsquares, cheesecakes, and pancakes all gluten free (most were not vegan though, so you might have to put in more trials to get good results)
• the only tough thing is puff pastry or phyllo dough; i've never seen a gluten free one for sale, let alone gluten free and vegan, you would have to do them yourself, but youtube has some good tutorials for everything, i was teaching myself the phyllo dough one just last night and while it will take forever, i can now make gluten free baklava
• be careful with things that should be gluten free like potatoes: lots of fries and wedges from restaurants are coated in flour before they are frozen/fried, and lots of those that aren't coated are fried in the same deep-fryer that cooks breaded things, some places have a fryer dedicated to only gluten free things but ask before you order (many gluten free people are split on this one but only once in my life have i seen a perfectly clean deep fryer and that's because i cleaned and filled it myself before the restaurant opened)
• for any spreads you eat like jam or peanut butter get a new one for yourself once you swap; lots of breadcrumbs end up back in the jars from scraping on toast and its honestly too much trouble to try teaching people to only scoop what they need for all their stuff then spread it without going back to the jar, just tell anyone you live with that your new one is off limits
• clean your dishwasher really well before you switch over; sometimes all the food scraps aren't drained out or it isn't sanitized properly if your dishwasher is old/shitty/hasn't been cleaned in a bit and this could have you ingesting old gluten for a while even if your new diet is perfect, since i live with people who aren't gluten free I just wash all my dishes by hand before i use them
• check things like your shampoos or medications, some people can be very irritated by wheat or oats in moisturizer or cosmetic products and it could be causing an issue you might have thought is unrelated
• looking up a product before you eat or buy it will become second nature, lots of blogs keep up to date on companies policies but trust what is or isn't on the label
• depending on what country you live in things may or may not be labelled gluten free, but also depending on what side of a border something is made it could have wheat contamination and not be marked or marked differently when imported (canada usa border is notorious for it, but likely other borders are similar)
• invest in a food processor; hummus is both gluten free and vegan and buying chickpeas and tahini to make it yourself will save you money over just buying containers of hummus, but you might also use it for mixing flours/adding something to your flours, or processing breads to make gluten free breading/panko, or vegan nut based milks or dressings