Had A Cough And Chest Cold For Two Weeks. Now

Had a cough and chest cold for two weeks. Now have had a sore throat and sinus infection for over a month. I've been to the doctor twice and got a z-pack and oral steroids and the sore throat and sinus infection persists. Also checked for asthma and allergies...results negative. Is this normal for these symptoms to drag on, should I go back to the doctor again?