How Can Bronchitis Along With Sinusitis Be Treated?

I have had bronchitis for the past few weeks initially it was diagnosed as sinusitis / bronchitis so i began a round of doxicyclone and the worst part was the constant uncontrollable dry cough with little sputum. I have been to urgent care every week and each doctor try s something new prednisone was used for a 10 day cycle and the last doctor gave me Robafen AC to help me sleep. My question is my face in the past few days has begun showing acme like blemishes on forehead and cheeks not itchy just red. Is this a normal body function because of the intense coughing spells?