Nephrotic Syndrome: This condition is characterized by significant proteinuria, hypoalbuminemia, and edema. The presence of bilateral leg swelling (edema) and petechiae (which could be related to a low platelet count or a coagulopathy secondary to nephrotic syndrome) makes it a strong candidate. Nephrotic syndrome can lead to a hypercoagulable state, increasing the risk of thrombosis, which might manifest as petechiae.

Immune Thrombocytopenic Purpura (ITP): ITP is an autoimmune disease that results in a low platelet count, which can cause petechiae. While it primarily affects platelets, it could be considered in the differential for a patient with petechiae, although the bilateral leg swelling would need another explanation.
Henoch-Schönlein Purpura (HSP): HSP is a form of vasculitis that affects small blood vessels and is characterized by palpable purpura, abdominal pain, arthralgias, and renal involvement. The presence of petechiae and leg swelling could fit this diagnosis, especially if there's a history of recent infection or other systemic symptoms.

Disseminated Intravascular Coagulation (DIC): Although less likely, DIC is a critical diagnosis to consider due to its high mortality rate. It involves both widespread clotting and bleeding and can be triggered by severe infections, trauma, or malignancy. Petechiae could be a manifestation of the bleeding aspect of DIC, and leg swelling could be due to underlying conditions leading to DIC or the coagulopathy itself.
Malignancy (e.g., Leukemia or Lymphoma): Certain malignancies can cause both petechiae (due to bone marrow infiltration affecting platelet production) and leg swelling (due to obstruction, infiltration, or secondary effects like nephrotic syndrome). These conditions are less common but critical to identify early.

Kawasaki Disease: This is an acute febrile illness of childhood that can lead to vasculitis, particularly of the coronary arteries. While it more commonly presents with fever, rash, conjunctivitis, and lymphadenopathy, it could potentially cause leg swelling and petechiae in rare cases.
Systemic Lupus Erythematosus (SLE): SLE is a chronic autoimmune disease that can affect multiple systems, including the skin, joints, kidneys, and blood vessels. It could potentially cause both petechiae and leg swelling, especially if there's renal involvement leading to nephrotic syndrome. However, SLE is less common in this age group and would typically be accompanied by other systemic symptoms.