Rib Fracture: This is the most likely diagnosis given the history of a fall, as rib fractures are a common consequence of blunt trauma to the chest. The pain is typically sharp and worsens with deep breathing or coughing.

Muscle Strain: The muscles between the ribs (intercostal muscles) can be strained during a fall, leading to pain. This diagnosis is likely if the pain is more diffuse and not localized to a specific rib.
Costochondritis: Inflammation of the cartilage that connects the ribs to the breastbone (sternum) can cause pain, especially if the fall resulted in direct trauma to this area.
Pneumothorax: Although less common than rib fractures, a pneumothorax (collapsed lung) can occur after a fall and cause rib pain, especially if there was significant trauma to the chest.

Hemothorax: Accumulation of blood in the pleural space can occur after a traumatic fall and is a life-threatening condition that requires immediate medical attention.
Pulmonary Contusion: A bruise of the lung tissue can result from a severe chest injury and may not be immediately apparent but can lead to significant respiratory distress.
Aortic Injury: Although rare, a fall from a significant height or a high-speed motor vehicle accident can cause an aortic injury, which is immediately life-threatening.

Osteomyelitis: Infection of the bone is a rare complication of a rib fracture and would typically present with additional symptoms such as fever and worsening pain over time.
Tumor: Metastatic disease to the ribs or a primary bone tumor could cause rib pain but would be an unusual first presentation after a fall without a known history of cancer.
Slipping Rib Syndrome: A condition where the ribs slip out of place, causing pain, is rare and might be considered if other diagnoses have been ruled out and the pain is reproducible with specific movements.