It absolutely gets better. I kept getting progressively less anxious every month, until now at 15 months I almost never get anxious.
The other day I was run off the road in my little Subaru by a huge truck who just didn't see me. In the past that would have skyrocketed my anxiety - but I just reacted and avoided an accident by ending up on the sidewalk and then the fear response passed within a minute or two. The best part about sobriety is lack of anxiety - and no more panic attacks.
I get over things really quickly now that I would have ruminated and worried and obsessed about for days and weeks when I was drinking.