It is hard to say exactly what this problem is. It is possible you had a prolonged viral infection (mononucleosis is an example of such infections), which can give the type of symptoms and prolonged course you have described. From your description, it does not seem like this is related to any problem in the lungs. It may be you had a sinus infection in the recent past, which set this off and is continuing to be a problem, despite the findings. I would work closely with your physician, perhaps culture the spot you can see and try to make a diagnosis. Then a course of action can follow.
Avoiding tobacco smoke and other irritants, good nutrition with plenty of fluids, rest and medication are all important in your recovery. If this were bronchitis, how long the acute bronchitis lasts is determined by your general state of health, your lung health, the virus or bacteria involved, ongoing exposure to tobacco smoke and how soon you get treatment. Frequent good hand washing and the use of disposable tissues can decrease the number of acute bronchitis infections.