Medial collateral ligament (MCL) sprain: This is the most likely diagnosis due to the mechanism of injury (fall) and the location of pain (medial knee). The MCL is commonly injured in valgus stress injuries, which can occur when the knee is bent and a force is applied to the outside of the knee, causing the MCL to stretch or tear.

Medial meniscus tear: The menisci are cartilage structures in the knee joint that can be injured in a fall, especially if the knee is twisted or bent. Medial meniscus tears can cause pain and stiffness in the medial knee.
Pes anserine bursitis: This is an inflammation of the bursa that separates the medial hamstring tendons from the tibia. It can cause pain and swelling in the medial knee, especially after a fall.
Medial knee contusion: A direct blow to the medial knee can cause a contusion, which can lead to pain, swelling, and bruising.

Fracture (e.g., tibial plateau or medial condyle fracture): While less likely, a fracture can occur after a fall and must be ruled out to avoid delayed diagnosis and treatment. A fracture can cause significant pain, swelling, and instability in the knee.
Vascular injury (e.g., popliteal artery injury): A severe injury to the popliteal artery can occur after a fall and can lead to limb-threatening ischemia if not promptly diagnosed and treated.
Nerve injury (e.g., saphenous nerve injury): The saphenous nerve runs down the medial aspect of the knee and can be injured in a fall, causing numbness, tingling, or pain in the medial knee and lower leg.

Osteochondritis dissecans: This is a rare condition where a piece of cartilage and bone in the knee joint becomes damaged and can cause pain and stiffness in the medial knee.
Medial knee tumor (e.g., osteosarcoma): While extremely rare, a tumor in the medial knee can cause pain and swelling, and must be considered in the differential diagnosis, especially if the pain is persistent and unexplained.