I assume that "c-diff" means Clostridium Difficile. This is an anaerobic bacterium that usually causes diarrhea. However it can cause respiratory infections, especially upper respiratory infections. Many antibiotics are effective against it including Vancocin® (vancomycin).
A cough that is productive of green sputum is worrisome. Your sputum should be cultured. Also you should have a chest x-ray. You may need to have a chest CT scan and maybe even a bronchoscopy. Actually, given the duration of this unexplained infection, you should seek consultation with an infectious disease specialist.