Your mind is going a million miles a minute because you are in early sobriety. That's part of it. I used to take ADHD meds too - when I was drinking - and now I don't.
Were you diagnosed as a child? I wasn't, it was part of the disease of alcoholism. The meds did help. I don't need them now. Does your doctor know about the amount of alcohol you use in addition to the ADHD meds? They aren't meant to be taken together and the doctor needs to have the whole picture.
The speedy brain calms down 99% with continued sobriety and prayer and meditation.
It. Takes. Time.
Time, meaning you have to get through the first months first. Every drink prevents healing. Acceptance of the fact I was physically healing was huge for me. My brain and nervous system needed a long time to "rewire" - to return to baseline. When I got that uncomfortable speedy brain thing, I exercised. Even if it was jumping jacks for two minutes - it worked. When I was drinking, and in the first few months of sobriety I used to think, "Well, I'm different. People don't understand." No. I had abused alcohol and messed up my body. It does return to normal with time.
Continuing to return to alcohol just keeps you sick. I promise you that with continued sobriety - long term - you will settle down. I had forgotten how good it feels to be able to relax, really relax. Just the other day I thought, "Wow, it's like being 12 again." My body has returned to healthy. I don't have crazy, neurotic, speedy, anxiety brain.
Edit, I just saw your last post. Do you have a copy of AA's Big Book? I don't go to meetings anymore, but the book is inspired. I think you would enjoy reading it. You can read it free online.