Final answer:
The osmotic fragility test is the appropriate diagnostic test to confirm the diagnosis of hereditary spherocytosis in a two-year-old boy with normocytic anemia and spherocytes on his blood smear.
Step-by-step explanation:
To confirm the diagnosis for a two-year-old boy who developed pallor following a viral upper respiratory tract infection and was found to have normocytic anemia with spherocytes on the peripheral blood smear, the appropriate test would be the osmotic fragility test. Spherocytes are often a sign of hereditary spherocytosis, and the osmotic fragility test is a diagnostic test specifically for this condition where the increased fragility of red blood cells to lysing in a hypotonic solution is examined. In contrast, the direct Coombs test would be used to identify autoimmune hemolytic anemias, hemoglobin electrophoresis would be appropriate for disorders such as sickle cell anemia or thalassemias, and serum reticulocyte count would indicate the bone marrow activity in response to anemia.