I Have A Very Dry, Non-productive Cough, No Fever, But

I have a very dry, non-productive cough, no fever, but on and off sweating. I was on prednisone for 5 days and than 5 days of a z-pack antibiotic for the last 2 weeks for a bad sinus infection. That seemed to clear up but moved to my lungs or chest. Not sure what to do now. I have tried 2 nebulizer treatments to get the cough productive, but that is not helping at all. What can I do?