I had a very serious alcohol problem in the past and I waited way too long to resolve it. But when I finally put my mind to it, definitely found peer support groups immensely helpful. This site/forum has tons of useful suggestions for recovery methods and it's a community on its own.
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I attended a bit of AA but it wasn't my favorite... SMART recovery was! They have a website with information, unfortunately the meetings are not as abundant as AA but if you live in a city, chances are you will find one. They also have online meetings. I found SMART great for relapse prevention and it has elements very similar to group therapy (it draws a lot from certain modalities). Another one I liked (and similarly not as well-known) is Refuge Recovery, if you are interested in a more spiritual approach but not the AA kind.

I had a therapist who claimed to have addictions as one of his specialties but he was completely useless in that domain, actually would have made my issues worse if I had let him. I believe there are better Ts but I personally did not find therapy useful to resolve the addiction and relapses. For many reasons, one major being that the urges to drink and relapses never happen when I had sessions and when I was not in that mindset, I had no issues thinking about my addiction clearly and understanding anything about it. We cannot think and talk ourselves out of it - probably why your T is also suggesting the support group. What's great about those is that they can be there and available anytime, they are not structured and compartmentalized like therapy... if you want them.

I had horrible, unbearable anxiety at the end of my drinking and also quite severe depressive episodes... or maybe something more akin to bipolar disorder. Turned out to be intimately linked to my alcohol abuse and, with sustained sobriety (100% abstinence) it all went away, except some mild anxiety that is pretty easy to manage without any particular treatment. It took a while though. What I would suggest is that you take action to tackle your drinking problem NOW, don't wait because the more we wait the more difficult it becomes... and there may be lasting consequences.

ETA: My therapists were amazingly under-informed about recovery methods and available groups etc. They actually learned from me about them more than the other way around. This was even true, to a lesser extent, about a pretty expensive and upscale rehab facility I went to once. Again, I am sure there are better educated Ts who actually keep up to date, but I've always found other addicts in recovery the best source of information, experience and support. I would emphasize people in recovery/recovered, not so much those that are at the same stage and still struggle a lot. You will always find folks at all stages of addiction in peer groups... what I had found the most useful is to gravitate towards those that have actually succeeded to overcome it long-term. Surely just having company can help but, I think, miserable company will unlikely to make a big difference in the direction of lasting improvement and healing.