It's great that you are working with your doctors with this. The most important thing you can do is be honest with them. If you had been taking meds for your anxiety, you will find that, in time, they should begin working better for you.
As anxiety seems to be the "trigger" for your drinking, it is obviously important that you address the causes of anxiety in your life and work on how to address them. Therapy, both group and individual, can be helpful, if you are not already doing it.
We also have forums here on SR specifically for Anxiety
Anxiety Disorders - SoberRecovery : Alcoholism Drug Addiction Help and Information and Secular Recovery
Secular Connections - SoberRecovery : Alcoholism Drug Addiction Help and Information
They tend to not be nearly as active as Newcomers, but you'll find people who can address some of your questions a bit more specifically though.
Glad you found us. Welcome. Take care.