Cellulitis: This is a common bacterial skin infection that can cause swelling, pain, and induration of the affected limb. The presence of redness, warmth, and tenderness along with systemic symptoms like fever would support this diagnosis.

Deep Vein Thrombosis (DVT): DVT can cause swelling and pain in the arm, especially if it occurs in the upper limb. Risk factors such as recent surgery, immobilization, or cancer would increase the likelihood of this diagnosis.
Lymphedema: This condition involves the abnormal collection of protein-rich fluid in the interstitial tissue, leading to swelling of the arm. It can be primary (inherited) or secondary (due to surgery, infection, or trauma).
Insect Bite or Sting Reaction: Certain insect bites or stings can cause localized swelling, pain, and induration, especially if there is an allergic reaction involved.

Necrotizing Fasciitis: Although rare, this is a life-threatening infection that requires immediate attention. It causes severe pain, swelling, and induration, often with systemic signs of infection.
Compartment Syndrome: This condition involves increased pressure within a muscle compartment, leading to pain, swelling, and potentially permanent damage if not promptly treated.
Venous Obstruction: Obstruction of the venous system, such as superior vena cava syndrome, can cause swelling and pain in the arm, and it is crucial to identify and treat the underlying cause.

Lipodermatosclerosis: A condition characterized by inflammation and scarring of the subcutaneous fat, leading to swelling and induration, typically seen in the context of chronic venous insufficiency.
Erythema Nodosum: An inflammatory condition that can cause painful nodules, usually on the lower extremities but occasionally on the arms, often associated with systemic diseases or infections.
Sarcoidosis: A systemic disease that can cause granulomatous inflammation in various parts of the body, including the skin, leading to swelling and induration, although arm involvement is less common.