Wrist Sprain: This is the most likely diagnosis given the presentation of a wrist sprain. The mechanism of injury, such as a fall onto an outstretched hand, can lead to stretching or tearing of the ligaments in the wrist, resulting in pain, swelling, and limited mobility.

Wrist Strain: Similar to a sprain but involves the muscles or tendons rather than ligaments. Overuse or direct injury can cause strain, leading to pain and dysfunction.
Scaphoid Fracture: A common fracture in the wrist, especially after a fall onto an outstretched hand. It might not always be immediately apparent on X-ray, making clinical suspicion crucial.
Triangular Fibrocartilage Complex (TFCC) Injury: The TFCC is a ligamentous structure on the ulnar side of the wrist. Injury to this area can cause ulnar-sided wrist pain, especially with rotation and gripping activities.

Compartment Syndrome: A serious condition that occurs when pressure within the muscle compartments increases, potentially leading to muscle and nerve damage. It is a medical emergency requiring prompt intervention.
Ganglion Cyst Rupture: While not typically an emergency, a ruptured ganglion cyst can mimic an acute injury and should be considered in the differential diagnosis to avoid missing other serious conditions.
Infection (e.g., Septic Arthritis): Though less common, infection in the wrist joint can present with acute pain, swelling, and decreased mobility, similar to a sprain. It requires urgent medical attention.

Kienböck's Disease: A rare condition characterized by the collapse of the lunate bone in the wrist, often due to poor blood supply. It can cause chronic wrist pain.
Pisotriquetral Joint Disorders: Disorders of this small joint in the wrist can cause ulnar-sided wrist pain but are less common and might be considered after other diagnoses have been ruled out.
Tumor: Though extremely rare, a tumor in the wrist could cause pain and swelling, mimicking a sprain. It would be an unusual presentation but should be kept in mind during the diagnostic process.