Ligament Sprain or Meniscal Injury: The presentation of knee swelling, particularly lateral and above the patella, with limited mobility but without redness or hotness, suggests a mechanical or traumatic cause. Ligament sprains or meniscal injuries are common in such scenarios, especially if there's a history of trauma or sudden twisting injury.

Osteoarthritis (OA): OA can cause knee effusion, pain, and limited mobility. The absence of redness and heat does not rule out OA, as it is typically a chronic, non-inflammatory condition.
Bursitis: Prepatellar or suprapatellar bursitis could cause swelling above the patella. Although bursitis often presents with localized redness and warmth, chronic cases might not exhibit these signs.
Patellofemoral Pain Syndrome: This condition causes pain around or behind the patella, often related to activities that put stress on the knee, like climbing stairs, squatting, or jumping. Swelling might not be as prominent but could be present.

Septic Arthritis: Although the absence of redness and heat makes septic arthritis less likely, it is a critical diagnosis not to miss due to its potential for severe and rapid joint destruction. Any suspicion of infection, especially in immunocompromised patients or those with a history of joint surgery, warrants immediate investigation.
Spontaneous Hemarthrosis: This condition, often associated with hemophilia or anticoagulant use, can cause sudden onset of knee effusion and pain without trauma. It's crucial to consider in patients with a relevant medical history.
Osteonecrosis: While less common, osteonecrosis (avascular necrosis) of the knee can cause pain and swelling. It's particularly important to consider in patients with risk factors such as long-term corticosteroid use or excessive alcohol consumption.

Synovial Chondromatosis: A rare condition characterized by the growth of cartilage in the synovium, leading to joint swelling and pain. It might cause a chronic effusion and could be considered if other diagnoses are ruled out.
Pigmented Villonodular Synovitis (PVNS): A rare disease that causes the synovium to thicken and overgrow, leading to knee swelling, pain, and potentially hemarthrosis. It's a diagnosis to consider if there's recurrent hemarthrosis without a clear cause.
Neoplastic Conditions: Rarely, knee swelling and pain can be the first presentation of a neoplastic condition affecting the bone or soft tissues around the knee. While uncommon, it's essential to keep this in the differential, especially if the patient has risk factors or if the condition does not respond to typical treatments.

Clinical Examination: A thorough examination to assess the range of motion, stability, and specific tests for meniscal or ligamentous injuries.
Imaging: X-rays to rule out fractures or osteoarthritis, and potentially an MRI for detailed assessment of soft tissues, including ligaments, menisci, and cartilage.
Aspiration of the Knee Effusion: To check for infection (septic arthritis), hemarthrosis, or other conditions like gout or pseudogout.
Treatment will depend on the diagnosis but may include physical therapy, pain management, bracing, or in some cases, surgical intervention.