In my 14th year of sobriety depression took me to the point I couldn't get out of bed. I couldn't even kill myself. My shrink had taken me off an anti-depressant and I had to wait three weeks to take anything else. He started me on Wellbutrin & Effexor which worked beautifully. Depression lifted, hasn't been back in seven years. It takes time for all medication to work, sometimes over a month.
It's the norm for alcoholics to suffer from other mental illnesses like bi-polar and depression. It sounds like you're in very good, safe hands. I was as bad as you (doctor tried to get me to admit myself but I refused) and have a very good life today.
Hope this helps. When we're in deep "depression-think" it's almost impossible to believe we may get better ... here's a reminder that it really does.