A 62-year-old female presents to the outpatient clinic with escalating severe, generalized abdominal pain approximately 6 hours after an elective screening colonoscopy. She reports a new onset of nausea but denies vomiting or fever. On examination, she is tachycardic at 110 bpm and hypotensive with a BP of 90/60 mmHg. Her abdomen is rigid, globally tender to palpation, with rebound tenderness and guarding, particularly pronounced in the right lower quadrant. Bowel sounds are absent. She appears acutely ill. Given these findings, what is the most appropriate initial management strategy, and what critical complication must be actively excluded?