I have a very similar experience.
I started anti anxiety meds (along with another med to help urges) about 3 months ago. I have noticed my anxiety has decrease and so did my urges. I still have triggers and urges... and I also know I can not safely have a drink, because 1 is never enough for me.
Either way, I absolutely was drinking to help my anxiety. I also was drinking to stop withdrawal symptoms, because I was addicted and I gave into triggers/urges.
Congrats on seeking the medical advice, it seems that it is overall helpful. Which- I know, is a good feeling.