Suggest Remedies For Persistent Phlegm Production Despite Taking Medication

Hello, for more than several months, I have had a problem with my throat constantly having wet feeling phlegm/mucous that just sits there most of the time. I take blood pressure, so I talked to my local pharmacy about it and at her suggestion, I started to take Mucinex DM to try to bring it up, but it did not work. After trying Mucinex DM, I was traveling/airplane to New York in October 2016. While on the airplane, I developed a sinus headache and a hoarse voice my voice was gone quickly) so I went to another pharmacy at Duane Read who told me to take Mucinex D. I took it and it took care of my sinus headache quickly, but my voice took the whole week to get better; yet, it never got completely clear of phlegm/mucous. I went to my doctor when I came back from New York, and my Dr. prescribed the z pack. I took it exactly as told, and it did not help at all. So I went back to my doctor, and he prescribed the Cefuroxime Axetil 500 mg Table. I have not taken this yet because I looked at the side affects. I don t want a yeast infection which is what happened with the z pack, and then to take something else that may not work. What I wanted to ask is before I take this, is there a better way to solve my problem, maybe something more natural to clear my throat? For months I have been coughing or trying to clear the plegm/mucous from my throat.