How Do I Get Rid of My Phlegm and Cough?

Question

I am having no trouble managing asthma all because of Advair and a lesson on deep breathing. The problem is, I have a large amount of phlegm which never seems to clear itself from throat and low cough that doesn’t want to leave my body for some strange reason. No troubles sleeping though it’s the only thing I can do properly.  Has anybody encountered something like this? Any tried techniques for curing this menacing thing?