A 48-year-old woman presents to the acute care clinic complaining of excruciating, sharp abdominal pain that suddenly worsened an hour prior and now radiates to her right shoulder. She reports a long-standing history of intermittent epigastric discomfort, which has been more frequent recently after increasing her intake of over-the-counter ibuprofen for a knee injury. On examination, she appears distressed, lying still on the stretcher. Her vital signs are: temperature 38.20C, blood pressure 90/50 mmHg, pulse 130/min, and respirations 28/min. Her abdomen is rigid and board-like, with generalized tenderness, exquisite rebound tenderness, and guarding. Bowel sounds are absent. An upright chest X-ray is obtained, which reveals free air under the right hemidiaphragm. Laboratory results include: White Blood Cell (WBC) count 18.5 x 10^9/L, Hemoglobin 135 g/L, Sodium 138 mmol/L, Potassium 4.0 mmol/L, Amylase 80 U/L, and Lactate 2.8 mmol/L. Considering the clinical presentation, physical findings, laboratory results, and radiographic findings, what is the most likely diagnosis and the immediate definitive management strategy?