Transient Synovitis: This condition is a common cause of hip pain and limping in young children, often following a viral infection. It is characterized by inflammation of the synovial membrane of the hip joint, leading to pain and limited mobility.

Idiopathic Leg Pain: Also known as growing pains, this condition is common in children and typically presents as intermittent, bilateral leg pain, but can sometimes be unilateral.
Trauma or Fracture: Given the age and potential for accidental injuries, a fracture or soft tissue injury should be considered, especially if there's a history of a fall or trauma.
Infection (Cellulitis, Osteomyelitis, Septic Arthritis): Bacterial infections can cause pain, swelling, and limping. The presence of fever, redness, and swelling would increase the suspicion for an infectious cause.

Slipped Capital Femoral Epiphysis (SCFE): Although more common in older children, SCFE can occur in younger children and is a medical emergency due to the risk of avascular necrosis if not promptly treated.
Malignancy (e.g., Neuroblastoma, Osteosarcoma): Though rare, malignancies can present with limb pain and should be considered, especially if the pain is persistent, worsening, or accompanied by systemic symptoms like weight loss or fever.
Juvenile Idiopathic Arthritis (JIA): This chronic autoimmune disease can cause joint pain, swelling, and stiffness, leading to limping. Early diagnosis is crucial for effective management.

Legg-Calve-Perthes Disease: A rare condition characterized by avascular necrosis of the femoral head, more common in children aged 4-8 years, but can be considered in a 3-year-old with persistent hip pain and limping.
Congenital or Developmental Conditions (e.g., Developmental Dysplasia of the Hip): Though typically diagnosed earlier, some cases might not be identified until the child starts walking and shows signs of limping or uneven skin folds.