Gastroesophageal Reflux Disease (GERD): This condition is characterized by stomach acid frequently flowing back into the tube connecting the mouth and stomach (esophagus). The symptoms of GERD, such as epigastric pain, back burning, and shortness of breath (due to acid reflux potentially triggering asthma-like symptoms or exacerbating existing respiratory conditions), align closely with the described symptoms.

Peptic Ulcer Disease: This includes both gastric and duodenal ulcers, which can cause epigastric pain. While back burning is less typical, it can occur, especially if the ulcer is located near the gastroesophageal junction. Shortness of breath could be a sign of a more severe complication, such as perforation leading to peritonitis or an acute abdomen, though this is less common.
Acute Coronary Syndrome (ACS): Although more commonly associated with chest pain, ACS can sometimes present with epigastric discomfort. The back burning could be referred pain, and shortness of breath is a common symptom due to decreased cardiac output or pulmonary congestion.
Pulmonary Embolism (PE): While PE primarily causes shortness of breath and chest pain, it can occasionally present with epigastric pain if the embolism affects the lower parts of the lungs. The back burning could be due to associated musculoskeletal strain or referred pain.

Myocardial Infarction (MI): Similar to ACS, MI can present atypically, especially in women, diabetics, or the elderly, with symptoms such as epigastric pain and shortness of breath. Missing this diagnosis could be fatal.
Aortic Dissection: This is a life-threatening condition where there is a tear in the aorta's inner layer. It can cause severe, tearing chest or back pain, which might be perceived as burning, and shortness of breath if the dissection involves the aortic arch or affects cardiac function.
Esophageal Rupture: A severe condition that can cause chest pain, epigastric pain, and shortness of breath due to mediastinitis or sepsis. It's a medical emergency requiring prompt intervention.

Pancreatitis: While it typically causes severe abdominal pain radiating to the back, pancreatitis can occasionally present with epigastric pain and shortness of breath, especially if there's associated pulmonary involvement or severe metabolic disturbances.
Herniated Diaphragm: This can cause epigastric pain and shortness of breath due to the mechanical effects of herniated abdominal contents on the lungs and diaphragm. It's a rare condition but should be considered in the appropriate clinical context, such as after trauma.