Peptic Ulcer Disease (PUD): The patient's symptoms of gnawing constant pain in the left upper quadrant (LUQ), nausea, and anorexia are classic for peptic ulcer disease. The pain is often described as burning or gnawing and can be accompanied by nausea and vomiting.

Gastroesophageal Reflux Disease (GERD): GERD can cause similar symptoms, including chest and upper abdominal pain, nausea, and anorexia. The pain can be constant and gnawing, especially if there is an associated ulcer.
Gastritis: Gastritis, or inflammation of the stomach lining, can cause upper abdominal pain, nausea, and anorexia. The pain can be constant and gnawing, similar to PUD.
Pancreatitis: Pancreatitis can cause severe, constant abdominal pain that radiates to the back, as well as nausea and anorexia. While the pain is often more severe and radiates to the back, it can be considered in the differential.

Myocardial Infarction: Although the pain is in the LUQ, myocardial infarction can present with atypical symptoms, including epigastric pain, nausea, and anorexia. It is crucial to consider this diagnosis, especially in patients with risk factors.
Pulmonary Embolism: A pulmonary embolism can cause sudden-onset chest pain, nausea, and anorexia. While the pain is often more pleuritic, it can be considered in the differential, especially if there are risk factors.
Aortic Dissection: An aortic dissection can cause severe, tearing chest pain that radiates to the back, as well as nausea and anorexia. Although the pain is often more severe and radiates to the back, it can be considered in the differential.

Gastric Cancer: Gastric cancer can cause upper abdominal pain, nausea, and anorexia, but it is a rare diagnosis and often presents with weight loss and other systemic symptoms.
Splenic Infarction: Splenic infarction can cause severe, constant LUQ pain, nausea, and anorexia, but it is a rare diagnosis and often associated with underlying conditions such as sickle cell disease or vasculitis.