Transient Synovitis: This condition is a common cause of hip pain in children, especially in the 3-10 year age range. It is characterized by inflammation of the synovial tissue surrounding the hip joint, leading to pain and limited mobility, which matches the patient's symptoms of hip pain, limited internal rotation, and pain worsened by movement.

Legg-Calve-Perthes Disease: A condition where the blood supply to the growth plate at the end of the femur (thigh bone) is disrupted, leading to necrosis of the bone. It typically affects children between 4-8 years old and can cause hip pain and limping.
Slipped Capital Femoral Epiphysis (SCFE): A condition where the growth plate is weakened, and the femoral head slips out of place. It is more common in early adolescence but can occur in younger children, especially those who are overweight. Symptoms include hip, thigh, or knee pain and a limp.
Septic Arthritis: Although the patient does not have fever or other systemic symptoms, septic arthritis cannot be ruled out entirely without further investigation. It is an infection within a joint, which can cause severe pain, limited mobility, and systemic symptoms like fever.

Malignancy (e.g., Osteosarcoma, Ewing's Sarcoma): Although rare, bone cancers can present with pain and limping. Early diagnosis is crucial for effective treatment.
Osteomyelitis: An infection of the bone that can cause pain, fever, and limited mobility. It requires prompt antibiotic treatment to prevent long-term damage.
Juvenile Idiopathic Arthritis (JIA): An autoimmune condition that can cause joint pain and inflammation. While less likely given the acute presentation, it's a diagnosis that should be considered, especially if other symptoms develop.

Gaucher's Disease: A genetic disorder that can lead to bone pain and other systemic symptoms due to the accumulation of harmful substances within cells.
Sickle Cell Disease with Avascular Necrosis: In patients with sickle cell disease, avascular necrosis of the femoral head can occur, leading to hip pain and limited mobility.
Leukemia: Certain types of leukemia can cause bone pain due to marrow infiltration. While rare, it's a critical diagnosis to consider in the differential for unexplained bone pain in children.