Pancreatitis: The pain pattern described, with central abdominal pain radiating to the back, is classic for pancreatitis. The involvement of the left side could indicate the tail of the pancreas is affected.

Peptic Ulcer Disease: While peptic ulcers typically cause epigastric pain, they can radiate to the back and, less commonly, to the left side if the ulcer is located in a specific area of the stomach or duodenum.
Gastroesophageal Reflux Disease (GERD): GERD can cause central chest and abdominal pain that may radiate to the back and sides, although it's less common for it to radiate to the left side specifically.
Diverticulitis: If the diverticula are located in the sigmoid colon, which is on the left side, diverticulitis could cause left-sided abdominal pain that radiates to the back.

Aortic Dissection: Although less common, aortic dissection is a life-threatening condition that can cause severe, tearing pain in the chest and abdomen that radiates to the back. The pain can be on one side if the dissection involves a branch of the aorta.
Ectopic Pregnancy: In women of childbearing age, ectopic pregnancy can cause severe abdominal pain that may radiate to the back and sides. It's a medical emergency.
Ruptured Abdominal Aortic Aneurysm (AAA): Similar to aortic dissection, a ruptured AAA can cause severe abdominal and back pain and is immediately life-threatening.

Splenic Infarction or Rupture: These conditions can cause severe left upper quadrant pain that radiates to the left side of the abdomen and back. They are less common but can be associated with specific risk factors like trauma or sickle cell disease.
Left Kidney Stone or Pyelonephritis: While kidney stones typically cause flank pain, and pyelonephritis causes flank pain and fever, in some cases, the pain can radiate to the abdomen and back, especially if the stone is moving or the infection is severe.