Welcome ljc!
I experienced noticeable anxiety after I quit. It showed up in the first few weeks after quitting (4-6 weeks), in the form of feeling extremely uncomfortable in certain work situations, especially socialising at work functions. It was situation specific so I ignored it. Anyway, I had overall benefits from quitting, and felt so much better, i.e. clear-headed, fitter, stronger and so on, that the anxiety was "easy" to set aside.
Several months in, I had a few more experiences of hyperventilation, fast heartbeat, racing thoughts etc., in situations involving public speaking and presenting. It was noticeable and I was concerned it would be a hindrance at work. I was quite bothered. I could not remember experiencing this before ... and I felt a bit like I should not be experiencing it because ... well, c'mon, I was sober! Sober people (in my simple thinking) would not have such issues.
I opened up on SR and received some excellent suggestions from people here. The one that helped me most was deep breathing exercises which I now do before speaking in public. If you google "deep breathing anxiety exercises" or something like that, you'll see a bunch of helpful links.
I also run regularly, as if it is a form of prescribed medication, because that so-called runner's high is a dose of endorphins to my system which allows my body and mind to operate more smoothly. Perhaps it's a dependency but I have no better alternative at this point.
In time, the anxiety episodes have decreased. Part of it may be physiologically being further down the track of sobriety, part of it may be active management (breathing, running etc.), part of it may be simply being more comfortable with my work situation ....
Whatever the case, I do believe there's a good chance your symptoms will improve. It may be worth seeing a professional to discuss it.
Congratulations on the 3+ months of sobriety! It gets better, and better, and better!