Anxiety is worse now that I'm sober — is that normal?

Very normal, and worth taking seriously at the same time. Alcohol was muffling the anxiety while quietly making it worse — take away the muffler and you hear the engine. For a lot of people it settles considerably over the first months. AND: 'co-occurring' anxiety is extremely common and very treatable, so please say what you wrote here to a doctor or counselor — treating both sides together is the standard now, and nobody hands out medals for suffering through it untreated. In the meantime, the boring things are real medicine: sleep, movement, less caffeine than you think you need.