I think there might be other support groups for alcoholics if you don't like AA. Not everyone likes the 12 step method. I'm not an alcoholic, but I go to support groups for people with mental illnesses. There are no steps, but we talk about how we're doing and give each other support. It's really helpful to me.
If you're in the US, try dbsalliance.org or nami.org. They provide a lot of resources, and you can find support groups. Ptangptang has a good idea about exercise. Joining some sort of club to meet people and not isolate can also help.
When I'm anxious, I have found coloring can help. I know it sounds kind of silly, but there are adult coloring books you can get. Yoga and meditation can also help.
Hang in there. I hope you can find a positive coping mechanism.