Don S posted some alternatives to AA that might address your underlying problems better, it sounds weird to me your therapist doesn't know about those, but oh well, that aside I got nothing to add to what everybody already said, except maybe that I do relate pretty much, but here free mental health care is so disorganized you see a therapist for like 3 sessions and then you move on, imo it's impossible then to offer proper help but oh well I dun wanna hijack this thread into one of my famous rants again.
for taking such a huge step, always keep in mind how
you and nobody else could benefit from a certain treatment, therapy, whatever. Sometimes it might take a while for things to figure themselves out, but they always will, promise.
Marte