HI, thanks for using healthcare magic
A cough related to viral infection can last up to 6 weeks in some persons.
Since the cough is a productive cough, you may want to consider the use of a mucolytic
to help break up the mucus. Examples are bisolvin, acetylsteine, carbocysteine, guiafenesin.
There are other causes, other than colds for productive coughs such as sinusitis
. If you have a history of sinus problems , you may want to consider the use of a topical steroid nasal spray
and an antihistamine.
I hope this helps