I don't know how long you've been sober but if you can't string together a few months then its hard to know where your alcoholism ends and your anxiety begins, ya know?
As far as brain chemistry, I'm pretty sure Xanax doesn't really address that. Its really just alcohol in pill form (as are all benzo's). It just gets ya tipsy. Xanax acts very quickly, like taking a shot, and wears off quickly. Stuff like Ativan acts more slowly and stays in the body longer. Maybe talk with your dr about an SSRI or the like that actually will effect brain chemistry I believe. They never worked for me but that doesn't mean they won't for you.
If you can't get ahead of this have you ever thought of entering a true dual diagnosis treatment facility where they can work with you on both your addiction and the anxiety? Seems you have to get ahead of it somehow...