Cough for 20 days. Dx andcontinue!

First of all I've a smoking history of 3years and 5 cigerettes a day... 20 days ago I made a trip to a place after which I got cough. After 7 days of persistent and bad cough with white sputum I visited a doctor... She prescribed me t. Augmentin-625 (1-0-1),t. Pan 40(1-0-1) and ascoryl E syrup for 3 days... and the cough didn't subside with these meds. After 3 days I visited again and got a new prescription : T. Kefpod 200mg(1-0-1),t. Montair lc(0-0-1),t. Rantac150mg(1-0-1) and a grillintus syrup for next 7 days along with a chest x-ray and sputum culture test. The chest x-ray ray was fine. But the sputum test couldn't be done as I didn't cough any sputum in mornings. My cough subdued alot in next 7 days. And I quit smoking too. But a little cough with a sore throat was still there so I visited again and they gave me t. Azythromycin500mg(1-0-1),t. Rantac(1-0-1) and ascoryl d syrup for next 3 days. And the sore throat is gone but cough is still there.they gaveme asthaxind dx andcontinue