Can anxiety disorders (like social anxiety)cause misophonia? or could it be a side effect of carbamazepine?

Yes and very rarely: Yes, I'd think it quite possible for anxiety disorders to cause extreme discomfort associated w/ sound and, That medications can cause irritability which would make you even more intolerant. Also, in very rare cases hearing oddities can be a side effect - i.,e. pitch perception, ringing, etc. Talk w/ the doctor about it. Best!