Welcome to SR, Kathryn!!!!
You will find lots of support here. I am very similar to you, in that I have been in and out of AA for the past 3 or so years (but I'm a bit older...38). I, too, have only been able to maintain very short periods of sobriety in the past few months, and I also deal with depression and anxiety.
I have found that the depression and anxiety make me want to drink, but when I do drink to "self-medicate," it makes my anxiety sooooo much worse and more difficult to deal with!
You will find lots of support and wisdom here at SR. I am on day 4 (again) and check the site every day at least twice a day for support and wisdom and encouragement. Check out AA meetings (empty your head of the past experiences and allow a new appreciation for the wisdom to permeate your mind) as well as other recovery tools, such as Rational Recovery and SMART recovery.
Getting sober and staying sober and Thriving in sobriety entails a complete change of lifestyle. I would also recommend incorporating some sort of excercise into your recovery plan, as it is tremendously helpful for depression and anxiety!