I don't mean to drag anyone in these comments but Pinterest and its consequences have been a disaster to the human race.

Vinegar and baking soda are not a useful combination to use when cleaning. It produces: sodium acetate and carbon dioxide bubbles.

Sodium acetate is of such marginal use in cleaning that it might as well not be used in the first place (think along the lines of sprinkling a little table salt into water to "improve" the cleaning action).

Carbon dioxide bubbles, except in a couple of cases, pretty much as useless as sodium acetate; if you disagree, would you pour sparkling water down a drain and expect much of anything to happen? Because that's basically what a solution of baking soda and vinegar or lemon juice achieves.

On their own, vinegar or baking soda are much more useful as cleaning agents.

Vinegar is decent for use as a general surface cleaning agent and for mild rust stains or hard water/mineral build-up.

Baking soda or, preferably, washing soda is decent for use to break down grease or and oily stains. It's also really good at softening things so if you have stuff burnt in the bottom of a pan that won't lift easily, a good amount of either (washing soda is approximately 2x as effective as baking soda) with enough water to cover the burnt parts, brought to a boil and left to sit for at least an hour but maybe overnight if necessary works a treat.

But draino is usually caustic soda - itself much stronger than either baking soda or washing soda.

There are typically three different types of clogs you will find in a sink:

• Debris

• Fats and grease

• Mineral build-up

Mineral build-up is the least likely to occur. This likely requires a plumber to address although strong acids and mechanical cleaning (scrubbing or scraping) can address the problem.

Fats and grease tend to not occur in isolation unless you're pouring cooking oil down the sink. Don't do that unless your landlord is a fuckwit and know that if you do it, it's likely going to inconvenience you a lot so pick your timing appropriately. Fats and grease tend to accumulate on debris in the drain, such as strands of hair. Sodium hydroxide (lye or Draino [but make sure to check the packaging to ensure it has sodium hydroxide!]) will hydrolise hair, essentially dissolving it, and it saponify fats and grease thus making them soluble in water and helping to break up the grease which hasn't come into contact with the sodium hydroxide.

Don't use hot water to dissolve sodium hydroxide or it risks boiling over due to the heat produced when dissolving it. Always wear gloves and eye protection (even if it's just sunglasses) when using sodium hydroxide. Always add sodium hydroxide to water and not the other way around. Keep children and pets out of the room where you're using it.

Fats and grease can be dislodged by using boiling water, especially with a good amount of dish soap, but keep in mind that this can often just push the problem further down the line as it will soften up from the heat and flow down before cooling and resolidifying so if you opt for this, do so cautiously and consider using sodium hydroxide instead.

Debris is all the other stuff that clogs a drain, all the physical objects that probably shouldn't have gone down there in the first place. Most of the time this requires physically dislodging the blockage. Sometimes the weight of water is sufficient to dislodge debris but keep in mind that this risks pushing the clog deeper into your pipes, making it harder to deal with. Sometimes a plunger can achieve this same effect but the same caution applies. It is better to remove the pipe where the clog is and manually clear the blockage or to use tools to extract the debris.

Toothpaste is comprised of surfactants (think detergent) and it's readily soluble in water. If toothpaste has clogged in the sink and hardened, leaving water in it to soften it up should be enough to get it to break up by itself but it might need a bit of mechanical coaxing if it's really bad. But I suspect that it's probably that toothpaste is the final straw that clogged the drain and that you are likely dealing with hair and grease which are the major cause of the blockage.

If draino didn't work (Did you follow the instructions properly? How long have you left it to sit? Does your Draino contain sodium hydroxide?) Then the next step would be to try to clear the blockage, as described above. Note that if your pipes are full of draino then it's a hazard and you don't want to spill it everywhere by removing any pipes. You can neutralise Draino by adding vinegar until it stops fizzing but I can't tell you how much it would require or how much sink space you are left to work with here.

Good luck!

I picked up one these air pressure toilet plungers off aliexpress, it'll make easy work of toothpaste blobs:

https://www.aliexpress.com/item/1005005384704578.html?spm=a2g0o.productlist.main.21.77d94ab8hbVK5x&algo_pvid=dd3c9511-50e4-4aa5-b16f-fe32678e4aba&algo_exp_id=dd3c9511-50e4-4aa5-b16f-fe32678e4aba-10&pdp_npi=4%40dis%21CAD%2166.36%2144.46%21%21%2147.78%2132.01%21%402101c59517096881147842876e87bf%2112000032834818767%21sea%21CA%212334007332%21&curPageLogUid=zQZ32MwWhiEf&utparam-url=scene%3Asearch%7Cquery_from%3A

Run some boiling water through the drain then chase it with baking soda and vinegar, preferably you have some way to stopper the sink after adding the vinegar and confine the chemical reaction to the drain, give it maybe a hour and then dump in more boiling water. Ideally you want to do this kind of stuff before it becomes completely clogged because it's a lot harder to remediate it without physically taking the pipes apart or running a drain snake through it.

you can also, if you have a clean toilet plunger (or willing to use a dirty one) plunge the sink. keep in mind, if your sink has a hole in the side of the bowl for air, to cover up those holes while you plunge.

do this if you start running out of options. its not exactly healthy for your plumbing to do this regularly

Try a baking soda solution chased a little later with some distilled white vinegar.

Try boiling some water and pouring that down, then get a plumbing snake, they're like 20 dollars, may need to try different access sites, not just going straight into the pipe from the sink drain to clear the clog.

If you want to go stronger then draino Lye is pretty much your only good option. You can pick it up at hardware store, should be right with the draino.

There is going to be hair in there too. Try to find a barbed plastic clog cleaner that can snag those clumps and drag them out. Something like this thing:

https://www.homedepot.ca/product/hdx-2-piece-drain-cleaning-tool/1000818036