Fracture or Dislocation: This is the most likely diagnosis given the history of an injury. The pain and swelling are consistent with a fracture or dislocation, and numbness could be due to nerve compression or damage.

Soft Tissue Injury (e.g., Sprain, Strain): These injuries can cause significant pain and swelling, and if severe, could lead to numbness due to swelling compressing nerves.
Compartment Syndrome: This condition, characterized by increased pressure within a muscle compartment, can cause pain, swelling, and numbness, especially after an injury.
Nerve Injury: Direct damage to nerves during the injury could result in numbness, pain, and possibly swelling due to associated soft tissue injury.

Vascular Injury (e.g., Arterial or Venous Damage): Although less common, missing a vascular injury could lead to severe consequences, including limb loss. Symptoms might include coldness, pallor, pulselessness, poikilothermia, pain, paresthesias, and paralysis (the "6 Ps").
Infection (e.g., Cellulitis, Abscess): While less likely immediately after an injury, if the wound becomes infected, it could cause pain, swelling, and numbness due to nerve involvement or compression.
Complex Regional Pain Syndrome (CRPS): A condition that might develop after an injury, characterized by severe, persistent pain, and could also include swelling and numbness.

Tumor or Cyst: Although rare, a pre-existing tumor or cyst could become symptomatic after an injury, causing pain, swelling, and numbness if it compresses nerves or blood vessels.
Neurological Conditions (e.g., Multiple Sclerosis, Guillain-Barré Syndrome): These conditions are rare and less directly related to an injury but could present with numbness and, in some cases, pain and swelling if there is associated muscle weakness or atrophy.