What Causes Coughing Up Of Phlegm After Taking Antibiotics Of Sinusitis?

I ve had sinus pressure, ear pain, teeth pressure headaches for 3 months. I ve been to the dentist....deep cleaning that started all these symptoms. They as a routine put me on 7 days antibiotics. 6 weeks after still sick went to Dr. Chest is clear (X-Ray). She put me on another 10 days antibiotics. Now coughing choking snot like phlegm (especially mornings). Still feel like it is in back of my throat. Have tried netti pot 2-3 times, saline spray occasionally. I m sick and tired of being sick and tired! Any ideas? By the way they increased my thyroid dose, a lot, just prior to all this.