Pediatric Puzzler: Lymphadenopathy and nosebleeds in 2-year-old girl: Is anything as it seems?

A 2-1/2-year-old girl's adenopathy has not subsided five days after initiation of antibiotic therapy with amoxicillin and clavulanate potassium (Augmentin). And lately, she seems to be having "a lot" of nosebleeds.