Nothing will happen or change if you can't commit to full open sobriety, and that depends on your relationship with alcohol. Are you just looking to cut back or control it? Or at rock bottom?
Is it a daily need, where you're telling yourself (can be subconsciously), you need it to move forward with your day? Do you hide it, as in you go out of your way to make (best attempt) sure no one is aware of (they are).
If any of these were answered yes, see your PCP, and ask if there's anything that could be done to help with quitting alcohol alongside your anxiety/depression treatment.
Next let everyone you are close to know that you're attempting sobriety, family and close friends should do their best, to help back-up you up. If everyone is aware of it, then that's a large part of mitigating the anxiety during the process. A good support team helps a lot.
