I think seeing your doctor is a great idea and talking things through with them. I take anti anxiety meds and have done for years. Very mild prescription but it helps so much. Although my stopping drinking itself reduces anxiety hugely too
Most of the anti depressants/anxiety meds are not addictive. The benzos are but they are more prescribed for short term occasional use, in my experience. Please be honest with your doc so they are able to prescribe accordingly and/or refer for therapy.
Many congrats on 2 months