Hi Tai
As you can see there are two main experiences with alcoholism and anxiety.
If your anxiety started with your drinking, then stopping drinking often fixes the problem - no immediately...but eventually
If you anxiety predates your drinking (or even maybe was a cause of it) then obviously you're going to need to address that anxiety.
some people see their Dr or a counsellor...I didn't go that route myself tho. I found some breathing exercises helped me to deal with a lot of my anxiety - as did exercise.
I also found that the more I engaged with problems, instead of reatreating to the bottle, the more I thought of myself as capable and that fear of failure I used to have fell away a lot.
I'm not cured...but I'm the best I've ever been and I'm ok with that
Hope you find a solution that fits you
D