This is Dr. David
you could have bronchiectasis or inflammation and swelling of your airways.
you could have a viral infection of your lungs which doesn't respond to antibitoics
you could be having asthma or reactive airway disease.
you might need a course of steroid therapy pills to help decrease swelling of your airways to help decrease cough.
you might need an inhaler like a albuterol or nebulizer to help calm down your airways after this lung infection.