Spontaneous Rupture of a Hepatic Tumor or Hematoma: This condition is highly plausible given the large hepatomegaly, as tumors or hematomas can rupture, leading to acute abdominal pain, nausea, and vomiting.

Hepatic Vein Thrombosis (Budd-Chiari Syndrome): This condition can cause hepatomegaly and acute abdominal pain due to thrombosis of the hepatic veins, leading to liver congestion and potentially nausea and vomiting.
Acute Hepatitis: Although hepatitis typically presents with more systemic symptoms, severe cases can lead to significant hepatomegaly and abdominal pain, accompanied by nausea and vomiting.
Liver Abscess: A collection of pus in the liver can cause hepatomegaly, pain, and systemic symptoms like nausea and vomiting, especially if the abscess is large or ruptures.

Ruptured Abdominal Aortic Aneurysm: Although not directly related to hepatomegaly, a ruptured AAA can cause severe abdominal pain and should be considered in the differential due to its high mortality rate if missed.
Ovarian Torsion: In females, ovarian torsion can cause severe abdominal pain and nausea, and while it's not directly related to hepatomegaly, it's a critical diagnosis not to miss due to the potential for losing the ovary.
Ectopic Pregnancy: Another critical diagnosis in females, ectopic pregnancy can present with abdominal pain and nausea, and while it's not directly related to hepatomegaly, it's life-threatening if not promptly diagnosed and treated.

Amyloidosis: A condition characterized by the deposition of amyloid proteins in various organs, including the liver, leading to hepatomegaly. It can cause abdominal pain and other systemic symptoms, though it's less common.
Polycystic Liver Disease: A rare genetic disorder leading to the growth of numerous cysts filled with fluid in the liver, which can cause hepatomegaly and abdominal pain.
Primary Biliary Cholangitis: An autoimmune disease of the liver that can lead to hepatomegaly and abdominal pain, though it typically has a more chronic presentation.