I had this as well. I have to say, it gets worse. Much, much worse.
I got to the point I was on anxiety meds, which was pretty stupid given you aren't supposed to drink with them. I was having full on anxiety and panic attacks. It goes much further than feeling anxious with time. The meds stopped helping, the frequency and intensity will increase.
I will say it was the worst feeling I have ever experienced at the end. I could no longer live like that. It was shear desperation. I had to quit, or die. Those were the only two options.
I've been sober now 21 months. The anxiety is gone.
It was such a horrible thing that just thinking about it makes my skin crawl. That's a long way down from the martini bar at the Ritz... But sobriety is so much better!