There are secular AA programs. I attend a couple in my area, have found them to be extremely helpful as a support group, and would not label them as a "church group".

Physicians aren't a cure-all, because there's no guarantee they've been trained in addiction medicine. After a few doctor visits and them hearing the word "anxiety", you might just leave with a new prescription to Xanax or some other benzo, which could be a virtual death-sentence for someone with a dual-diagnosis.