I suffered both, CBT therapy has helped a great deal with the depression and anxiety, also learning some self acceptance. Actually I realized in the end that alcohol was only exacerbating the mental health issues, I had some terrible anxiety and depressive episodes before I stopped.
I have medical support, people who help me address these issues. At first I reasoned that the 12 steps weren't really relevant to me, but I do find a lot of the conventional material on alcoholism/addiction helpful. I let the professionals deal with the mental health side of things, but also involve myself in the other recovery resources around.