They make it so easy. NHS waiting lists can be years long. I was on a "9 month" waiting list for nearly a year. Since following the instructions here it has been 2 and a half weeks and my first appointment is about to be booked.
As long as your GP isn't an ass and accepts that your self-assessment form and any evidence you have is enough to justify an assessment, you will be able to get an appointment. You just give forms/letters to your GP and Psychiatry UK do the rest - even chasing payments from your CCG.
In my experience, GPs often aren't familiar with how Right to Choose works or confuse it with funding requests, which the CCG will likely decline. There is a letter you can print on the page I linked that outlines Right to Choose for the GP. I also edited mine to clear up that it wasn't a funding request and didn't require the same protocols.
Once your GP has sent your referral to P-UK, they will contact you. You then sign up to their portal where they will send you forms to be filled in. 3 are for you and one is an "informant form" for someone who knows you well. This is the only real difficult part because you might not have someone who knows you well enough/believes that you have it/ you could be like me and know your parents would just dismiss whatever you have to say about it.
Fortunately for me my gf is supportive and was willing to do it, I also asked P-UK if that was appropriate, they said "The Informant Report is ideally completed by someone who knows you well and has for some time." It's probably fine for say, a close friend who has known you for at least a few years and at least somewhat understands ADHD and knows you want to get diagnosed. (Also it's very funny comparing what they notice about your symptoms to what you notice)
I don't doubt that's what you experienced, and I've heard plenty of other people with ADHD say the same things. However, there are a few things in this that I feel like are a bit too specific to your personal experiences, so I'd just like to add a few things to give OP and others a more holistic view of ADHD.
Like I said, I have no doubt that you've personally suffered due to treatments you've received. However, ADHD is a spectrum, and different people with it are going to have different experiences and needs in how they live with their disabilities. Other people can share their experiences on the matter, both positive and/or negative, but personally, I probably would've dropped out of college by now if I didn't get meds. I'm incredibly inattentive, and I can barely focus on lectures or homework when unmedicated. Tbh, there's even a lot of thing that I enjoy that I can barely focus on, so for me treatment has done nothing but make my life better.
Once again, I've heard a lot of people with ADHD say this, especially about Adderall, so I've no doubt this's true. However, different meds have different effects for different people. Personally I've only ever been on dexmethylphenidate, and I've never experienced any zombification. Also, I would like to say that no one has to take meds if they don't feel like it. Sometimes they just aren't effective or the side effects just aren't worth it, and sometimes they just aren't necessary. So I would like to make clear that that I don't want anyone to feel like they have to be medicated, just like I don't want people to be scared away from taking medication.
ADHD is a spectrum ranging from super hyperactive to super inattentive. You sound very much on the hyperactive side of the spectrum, while I'm very much on the inattentive side, so our experiences with ADHD are going to be very different. And that's not to say I'm not hyperactive. I do display certain signs of hyperactivity on a regular basis, and in certain situations I can even become more like the stereotypical person with ADHD who's bouncing off the walls with infinite energy. However, my inattentive symptoms are orders of magnitude more prevalent than my hyperactive symptoms in my day to day life. With that said though, most people with ADHD are going to wind up somewhere more towards the middle of the spectrum between hyperactivity and inattentiveness, so unless someone is definitely to one side or the other, it's better they listen to both experiences otherwise they could get the wrong idea as to what exactly ADHD entails.
Edit: Also, just so that I'm explicitly clear about my intentions (and in case I didn't come across in the way I intended), I'm not trying to make you feel bad or invalidated or anything like that.
I'm pretty inattentive if something does not catch my interest. Like I get really into that thing I'm into. Get good at it than get bored. I always found learning in school straight up boring, impossible to pay attention to, and honestly easy.
And just FYI if you get your kids diagnosed with adhd or add they will force you to medicate them. Some school districts go so far as to call cps on the parents of they won't medicate the kid.
You can figure out how to manage these things with out meds and you should. Some of it may just be this isn't for your. If you can't study than maybe academia is not for you. Maybe wrenching on cars, farming, or some other pursuit is more up your alley.