Cellulitis: This is the most common cause of limb swelling accompanied by redness, tenderness, and edema. It's a bacterial skin infection that can spread rapidly and is often caused by Streptococcus or Staphylococcus species. The symptoms described are classic for cellulitis, making it the top differential diagnosis.

Deep Vein Thrombosis (DVT): DVT can cause swelling, pain, and discoloration of the affected limb. While it doesn't always present with redness and tenderness, these symptoms can be present, especially if there's associated inflammation.
Lymphedema: This condition involves the abnormal collection of protein-rich fluid in the interstitial tissue, leading to swelling of the limb. It can be primary (genetic) or secondary (due to surgery, infection, or trauma) and may present with tenderness and redness if there's an overlaying infection.
Trauma or Injury: Direct trauma to the limb can cause swelling, tenderness, and redness due to inflammation and possible infection of the injured area.

Necrotizing Fasciitis: Although rare, this is a life-threatening condition that requires immediate medical attention. It's characterized by necrosis of the fascia and can present with severe pain, swelling, and redness of the affected limb. Early diagnosis is crucial for survival.
Compartment Syndrome: This condition involves increased pressure within a muscle compartment, leading to muscle and nerve damage. It can present with pain, swelling, and tenderness of the limb and is a medical emergency.
Septic Arthritis or Osteomyelitis: Infection within a joint (septic arthritis) or bone (osteomyelitis) can cause limb swelling, redness, and tenderness. These conditions are serious and require prompt antibiotic treatment.

Erythema Nodosum: A type of skin inflammation that can cause red, tender lumps on the legs. It's often associated with an underlying condition such as an infection or autoimmune disease.
Lipedema: A chronic condition characterized by the abnormal accumulation of fat cells in the legs, leading to swelling and tenderness. It's more common in women and can be mistaken for lymphedema.
Kawasaki Disease: A rare condition that mainly affects children, causing inflammation in the walls of medium-sized arteries throughout the body. It can present with limb swelling, among other symptoms like fever, rash, and conjunctivitis.