I suspect there is something related to the institutional nature of schools; these are schools in Virginia and northward, maybe it's because the buildings crank up the heat (drying heat) strictly according to the calendar without regard to the actual (uncommonly warm) weather, and that the sort of heating they have in school buildings is different (maybe drier, more stifling) than what they'd have at home.
But when it began this past week in my son's building, which is a two year old building with a totally different type of heating system, I changed my opinion - I believe it is going to turn out to be viral --
The District did a great job of getting in experts in many fields to try to find a cause and solution.