I too have had problems with alcohol and depression, so know that you are not alone.
My suggestion is to find some sort of support for yourself. No matter what that support system is. It is a lot to take on all by yourself and often people tend to relapse into their old ways when trying to do it all on their own. I personally found a great mental health provider who specialized in addiction issues and GLBT health/relationships, in addition to other things. Tackling the depression might help you with stopping drinking and vice versa. If you can't find someone like that, find someone that you are comfortable with at the very least.
Groups can be helpful too. AA, 12-step groups, 16-step groups, SMART recovery groups, etc. are out there to help folks break the feeling of isolation and help them connect with helpful resources. There are also a lot of online support options, live-chat support groups, yahoo groups, etc. Also, check out some of the books by gay authors who have had addiction issues. That helped me out a ton! I really liked the book, "Dry" by Augusten Burroughs.
Whatever you do though, don't beat yourself up about it. All sorts of people have addiction issues from all walks of life. I know doctors, therapists, lawyers, ministers, teachers, etc. that have all dealt with it. Nobody set out to become an alcoholic or an addict, but it happened anyway. Hang in there, find some support and stay strong!