Fracture of the distal femur or proximal tibia: Given the mechanism of injury (fall from a bicycle) and the symptoms described (greatly swollen knee, painful to walk on, palpable bump, and diffuse tenderness), a fracture in this area is highly plausible. The location and nature of the symptoms align with common presentations of fractures around the knee in pediatric patients.

Ligament sprain or strain: The knee's ligaments could be injured from the fall, leading to swelling, pain, and difficulty walking. However, the presence of a palpable bump might suggest a fracture or significant soft tissue injury rather than a simple sprain.
Meniscal injury: Though less common in children than in adults, a meniscal tear could occur, especially with a twisting injury. Symptoms might include locking, catching, or giving way of the knee, in addition to pain and swelling.
Patellar dislocation or fracture: A direct blow to the knee or a twisting injury could dislocate or fracture the patella, leading to severe pain, swelling, and difficulty walking.

Vascular injury: Any significant trauma to the knee could potentially injure the nearby blood vessels, such as the popliteal artery. Symptoms might include pale or cool skin, diminished pulses in the foot, or ongoing pain out of proportion to the injury.
Compartment syndrome: Increased pressure within the compartments of the leg could lead to severe pain, pallor, poikilothermia, paresthesias, and pulselessness. This is a medical emergency requiring prompt intervention.
Infection (septic arthritis): Though less likely in the immediate aftermath of a trauma without an open wound, any break in the skin could introduce bacteria into the joint, leading to septic arthritis. Symptoms include severe pain, swelling, redness, and warmth of the joint, often with systemic signs of infection like fever.

Osteochondritis dissecans: A condition where a piece of cartilage and a thin layer of the bone beneath it become detached from the end of the bone because of inadequate blood supply. It could be precipitated by trauma and might present with knee pain and swelling.
Tumor (e.g., osteosarcoma): Though extremely rare and unlikely to be directly related to a recent trauma, a pathological fracture through a pre-existing bone tumor could present with pain, swelling, and a mass. This would be an unusual presentation for a tumor but should be considered in the differential diagnosis if other findings are atypical or if the patient has a history suggestive of a tumor.