do you smoke?
if so stop it.
You might be having allergic diasthesis.
ie you may have allergic nose with phlegm dripping down the throat and which causes the cough and irritation.
YOu should see an ENT specialist
and get done CT scan
nose and paranasal sinuses
to see for any disease in nose and sinuses.
You may require steroid
nasal sprays and antihistaminics and normal saline nasal sprays