It LITERALLY "just" means that his immune system was in high gear. Aka he was sick. And then almost better OR starting to get sick again.
What usually kicks an immune system into high gear?
The common cold.
Or any other kind of infection.
Including pseudo infections (when the body thinks its infected, but the microbes are actually dead)... Aka immunizations.
Since it was 2 weeks later... And they were still elevated... He had a "real" infection. Probably a cold, maybe an ear infection, or bronchitis, or other lingering infection, but probably just a 10 day minor cold.
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There are rare disorders that come along with increased immune response (Juvenile Rheumatoid Arthritis for example)... But if your little one is in daycare... Then expect to be sick 1 week out of every month, or 1 week well and 1 week sick.
Sick all the time WITH an elevated white count is actually a good thing. If he were sick all the time and had a low WBC count I'd be worried.