Constipation due to immobility and pain after a fall: This is likely because constipation is a common issue after falls, especially in elderly patients, due to decreased mobility, pain, and potential medication side effects. The left abdominal pain could be related to constipation or a direct result of the fall.

Musculoskeletal injury: The fall could have resulted in a musculoskeletal injury, such as a rib fracture or muscle strain, which could cause left abdominal pain and cough due to referred pain or splinting.
Pneumonia or pulmonary contusion: A fall can lead to trauma to the lungs, resulting in pneumonia or pulmonary contusion, which would explain the cough and potentially the left abdominal pain if the injury is low in the chest or involves the diaphragm.
Urinary retention: This could be a cause of abdominal pain and constipation, especially if the patient has a neurogenic bladder or prostatic hypertrophy.

Splenic rupture or injury: Although less common, a splenic injury from the fall could present with left abdominal pain and is a potentially life-threatening condition that requires immediate attention.
Pulmonary embolism: While less likely, a pulmonary embolism could occur after a fall, especially in patients with risk factors for deep vein thrombosis, and would present with cough and potentially abdominal pain if the embolism is large.
Abdominal aortic aneurysm (AAA) rupture: Although rare, an AAA rupture could present with abdominal pain and is a medical emergency.

Diaphragmatic rupture: A rare but serious condition that could result from a fall, presenting with abdominal pain and respiratory symptoms.
Gastrointestinal perforation: Although uncommon, a perforation could occur due to the fall, especially if there was pre-existing gastrointestinal disease, and would present with severe abdominal pain.
Pancreatic injury: Direct trauma to the pancreas from the fall could result in pancreatitis, presenting with abdominal pain.