I am currently having the same problem. Started out with a bad head cold, which became sinusitis. I took a z pack for five days which cleared out the infection. Next stage was a flare up of my asthma and chest congestion and a cough. I have had the cough now for a few days already. My physician says my lungs are clear and I just have a lot of congestion. Not much one can do apparently other than wait it out.
i can relate i got a cold oct 17 have been to dr 4 times theres nothing you can do but let it run its course, drs tell e meds are not helping this year and lots are coming back 3-4 times still sick, most i have talk to have had it at least 3 months, mine turned into asthma which i have never had before so i had to go on a inhaler to help me but am still coughing and whezing now and than. hang in there in couple months it get better . merry christmas