I'm not sure where you live, but here in the city where I live, they have two hospitals that have AA special purpose meetings geared towards people with mental health issues and alcoholism. They tend to run on the smaller side (at least, in my experience) and are more accepting about talking about issues pertaining not just to alcoholism but to mental health as well.

The other option is to supplement real-life meetings with online ones. I have attended online meetings as agoraphobia is one of the issues I live with, and just as these forums can be very supportive, so too can online meetings.