I've always had terrible anxiety issues. Trauma and anxiety were the 2 big reasons that I drank. I can tell you, for me, it took a lot longer than a few months of sobriety before my anxiety got measurably better. For me, it may have taken more than a year.
Almost 7 years in, the peace I've gained is measured by the one or 2 anxious days a month I have instead of the 1-2 less chaotic days I had when I was newly sober. It takes a LONG time for your brain to rewire itself. If there was one thing I could give people when they come through the doors of new sobriety it would be long term patience. This takes time. I can tell you with no hesitation that if you can hang in there, you will know a new peace in your life that you've never felt before.