Hamstring Strain: This is the most likely diagnosis due to the location of the pain (back of the knee) and the symptom of reduced knee flexion. Hamstring strains are common injuries that occur when one or more of the hamstring muscles (semitendinosus, semimembranosus, and biceps femoris) are stretched beyond their limit, leading to pain and decreased function.

Baker's Cyst: A fluid-filled cyst that causes a bulge and a feeling of tightness behind the knee, which can lead to pain and limited mobility. It is often associated with knee arthritis or other knee problems.
Meniscal Tear: A tear in the cartilage of the knee joint can cause pain, stiffness, and limited mobility, including difficulty flexing the knee.
Tendinitis: Inflammation of the tendons around the knee, such as the hamstring or popliteal tendons, can cause pain and stiffness in the back of the knee.

Deep Vein Thrombosis (DVT): Although less common, DVT is a potentially life-threatening condition that can cause pain and swelling in the leg, including the back of the knee. It requires immediate medical attention.
Popliteal Artery Aneurysm: A rare but serious condition where the artery behind the knee becomes enlarged, which can cause pain, swelling, and limited mobility.
Infection (e.g., Septic Arthritis or Osteomyelitis): Infections in the knee joint or bone can cause severe pain, swelling, and limited mobility, and require prompt medical attention.

Tumors (e.g., Soft Tissue Sarcoma): Rare tumors in the soft tissues around the knee can cause pain, swelling, and limited mobility.
Neurological Conditions (e.g., Peripheral Neuropathy or Radiculopathy): Certain neurological conditions can cause pain, numbness, and weakness in the leg, including the back of the knee.
Vascular Conditions (e.g., Popliteal Artery Entrapment Syndrome): Rare vascular conditions can cause pain, swelling, and limited mobility in the leg, including the back of the knee.