I Have Been Coughing For About 3 1/2 Weeks Now

i have been coughing for about 3 1/2 weeks now i was put on zithromax 500mg for 5 days and prednisone 10mg. I am still coughing to the point where i almost vomit at times. I know have a sharp shointing pain in my right side rib cage back when I cough. Also no fever. Was told I had acute bronchitis, acute upper respitory infection.