Anxiety and alcohol do not mix. If you can stop the alcohol your anxiety will get much better. You can't put out a fire with gasoline which is what you are trying to do. The alcohol will make your medication NOT work. The medication is going into your body but not working correctly because of your drinking however.......when you stop taking the meds your body will withdrawl and your symtoms will feel worse.
I have been on Lexapro and it has worked great. I have tried others. It's trial and error. You need to be completly honest with him.
He's going to tell you simply to quit drinking, let him know you feel you can't.
I wish you the best.