Considering the 25-year-old woman's 12-hour history of abdominal pain, migration to the lower right quadrant, anorexia, mild RLQ pain without guarding or rebound tenderness, and a two-month history of crampy pain and diarrhea, what specific diagnostic steps would you take to differentiate potential causes of her abdominal pain, and how would these findings inform your initial management strategy in the Emergency Department?