What could cause pain in my lower right side of my stomach....

Many Possibilities: If the pain is severe and accompanied by sudden onset and fever it may be appendicitis. If it is crampy and moves it may be a kidney stone. As you are a female gynecological causes including ectopic pregnancy or ovarian cyst are possibilities. You should see a physician for a work up.

Lots: Depends on how acute, how severe, duration, other symptoms, etc. Can be things like appendiciyis, ectopic pregnancy, pelvic inflammatory disease (infection), ovarian cyst, inflammatory bowel disease, ureteral stone, other. Some are emergencies, some are not. Any doubt, see md now.