I just finished bactrim (sulfamethoxazole and trimethoprim) ds for inflamed cyst, i also have been having chronic diverticulitis can these antibiotics treat diverticulitis same time?

Possibly: However if it is going to work you actually must have a confirmed diagnosis of acute diverticulitis, not chronic diverticulosis. You would need 14 days of antibiotics and a 6 week course of low/no fiber diet. My preference is to confirm diverticulitis by labs, exam and possible CT scan, then initiate the above treatment if confirmed. I prefer levaquin/metronidazole as a more effective antibiotic