Hi 
welcome, im glad you joined us.
I think your doing the right thing about speaking with your dr to get extra support, i also have alcohol addiction and mental health along with having tried 6 different antidepressants that havent worked, but there are lots of options im sure your dr will be able to help for your specific needs. And not drinking will help your mental, physical snd emotional health.
In my experience the anxiety calmed down slowly once i abstained from alcohol and my brain and body had time to balance out more, im still early days and i still suffer with anxiety but nothing like when i was actively drinking.
You have the desire to stop and you clearly want to which is good.
Id recommend more meetings especially as you mention they helped, definitely dont worry about talking everyone there understands how it feels to be new and you wont be pressured to speak.
Have you tried online meetings ?
Heres the link to a thread with more info on them check it out theres a 24 hr AA zoom meeting too.
Starting the journey is tough but we are all on a journey here together, your not alone so take the step and the rest will follow and life gets better. 