When you say ' I am STILL coughing with throat clearing' means it has been there since the surgery. Then ideally you ought to have seen your surgeon already and what have you been waiting for last 5 weeks?
But if you mean those symptoms were not there after surgery and developed later, it could be fresh infection. Because operated cavities take a month to 45 days to heal completely. Till then raw surface area can get infected. So this could be a fresh infection causing some discharge coming back to your throat leading to cough and repeated clearing of throat. So it is too early to decide that surgery did not solve your sinus problem.
You may need a course of antibiotic.
Anyway it is better to see your surgeon as he knows exactly what he did in your nose and sinuses
. So please consult him.
Wish you good health.