Gastroenteritis: This condition can cause left upper abdomen pain and may lead to a mild increase in anion gap due to dehydration and metabolic acidosis. The anion gap of 13 is slightly elevated, which can be seen in various conditions but is not extremely high, making gastroenteritis a plausible explanation given the symptoms.

Pancreatitis: Inflammation of the pancreas can cause significant left upper quadrant abdominal pain. While pancreatitis itself may not directly cause a significant elevation in anion gap, the associated dehydration and potential for ketoacidosis could contribute to an elevated anion gap.
Diverticulitis: Although more commonly associated with left lower quadrant pain, diverticulitis can sometimes present with pain in the upper abdomen, especially if the diverticula are located in the sigmoid colon, which can refer pain upwards. The anion gap could be elevated due to associated infection and metabolic derangements.
Peptic Ulcer Disease: Peptic ulcers can cause left upper quadrant pain and, in severe cases, lead to perforation or bleeding, which might result in metabolic acidosis and an elevated anion gap.

Diabetic Ketoacidosis (DKA): Although the anion gap of 13 is not extremely high, DKA can present with abdominal pain and should always be considered, especially in diabetic patients. It's crucial not to miss this diagnosis due to its high morbidity and mortality if not promptly treated.
Sepsis: Sepsis from any source can cause abdominal pain and metabolic acidosis, leading to an elevated anion gap. It's a critical diagnosis not to miss due to its potential for severe consequences.
Mesenteric Ischemia: This condition can cause severe abdominal pain out of proportion to physical examination findings and can lead to metabolic acidosis. It's a diagnosis that requires prompt recognition and intervention to prevent significant morbidity and mortality.

Lactic Acidosis due to Mitochondrial Myopathies: Certain rare genetic disorders can lead to defects in mitochondrial function, resulting in lactic acidosis and an elevated anion gap. These conditions might also cause abdominal pain due to muscle involvement.
Ethylene Glycol or Methanol Poisoning: These poisonings can cause an elevated anion gap metabolic acidosis and might present with abdominal pain among other symptoms. They are rare but critical to diagnose due to their specific antidotes and potential for severe outcomes if not treated promptly.
Ureteropelvic Junction Obstruction: While more commonly presenting with flank pain, in rare cases, this condition could cause referred pain to the left upper abdomen. The anion gap elevation might be related to dehydration or associated metabolic disturbances.