C. Necrotizing Pancreatitis: The bluish discoloration over the umbilicus (Cullen's sign) and in the flanks (Grey Turner's sign) is highly suggestive of necrotizing pancreatitis, especially in the context of abdominal pain following a drinking spree, which is a common trigger for pancreatitis.

A. Pancreatic Pseudocyst: While less likely than necrotizing pancreatitis to cause the specific skin signs mentioned, a pancreatic pseudocyst could potentially cause abdominal pain and, in rare cases, might be associated with skin discoloration if it becomes infected or ruptures.
B. Pancreatic Abscess: Similar to a pseudocyst, a pancreatic abscess could cause severe abdominal pain and might be considered in the differential, especially if there's suspicion of infection. However, it's less directly associated with the specific skin signs described.

Hemorrhagic Pancreatitis: Although not listed among the options, hemorrhagic pancreatitis is a condition that could potentially cause the described skin discoloration due to hemorrhage and would be critical not to miss due to its high mortality rate.
Abdominal Aortic Aneurysm (AAA): While not directly related to pancreatitis, an AAA could cause abdominal pain and, in the case of rupture, might lead to discoloration due to bleeding. This is a life-threatening condition that requires immediate attention.

Chronic Pancreatitis (D): Chronic pancreatitis is less likely to present acutely with the specific signs of bluish discoloration over the umbilicus and flanks. It's more associated with long-term abdominal pain, malabsorption, and diabetes mellitus.
Other rare causes of abdominal pain and skin discoloration: These might include rare vascular or gastrointestinal conditions. However, given the context of recent alcohol consumption, pancreatitis and its complications are more likely considerations.