Why do I have pain in the lower right side of my stomach?

Depends. Abdominal pain can be due to many reasons. Pain that increases in severity, persists, or goes away and keep coming back needs to be evaluated by a doctor. Right-sided pain is most likely from gas or constipation but may be due to appendicitis, ovarian cysts, or gallstones.
Checks for RLQ pain. Causes of recurrent abdominal discomfort as described may be identified by first addressing signs/symptoms so as to localize the organ involved: vaginal discharge or bleeding, alteration in periods, pregnancy risk? Fever, nausea, vomiting, altered stool pattern, blood with stool, tenderness, distension? Painful urination, blood in urine? Recent trauma, herniations? Age? Gender? Other risk factors?