Cough for more than 2-3 weeks should be evaluated properly. still my suggestions might help..your description leads me to thinking that its due to cold allergy...unless you get your sputum tested don't take any antibiotics, consume warm water and thick soups frequently, hot beverages recommend 2-3 times a day. Stay warm. Anyways it could also be ATYPICAL ASTHMA, so first get evaluated once. No need to go again n again. Consult a respiratory physician he will examine and let you know further.