The presentation of severe epigastric pain with vomiting and a rigid abdomen strongly suggests peritonitis due to intra-abdominal contamination. A perforated peptic ulcer leads to gastric or duodenal content leaking into the peritoneal cavity, causing a rigid and tender abdomen (sign of peritoneal irritation). This acute surgical abdomen requires urgent diagnosis and management. Other options, such as acute cholecystitis or pancreatitis, typically do not present with a rigid abdomen. Immediate surgical consultation and imaging are essential for confirmation and treatment.

Reference: Bailey & Love’s Short Practice of Surgery, R. C. Russell, 27th Edition.