Hi, I hope it’s not too late for me to reply to your message!
What part of the UK do you live in? I’m in the south, and was very lucky to find that my GP was able to write to a funding body to handle my ADHD diagnosis and treatment. This was sadly not the case up north, where I was told I would need to pay £400 for a private diagnosis.
My advice is that whichever avenue you need to take, DO get the diagnosis. £400 is a lot, but it’s lifechanging if a positive result. My ADHD drugs are prescribed through a private doctor that is working with my GP, as far as I know you’re right that the NHS itself doesn’t prescribe ADHD meds.
If you have to go private and have the means to do so I recommend it, it’s worth saving for, but I know it’s a lot of money.