I have long suspected it is allergies, because it happens every single year around the same time which is a big part of why I haven't kept her home in the past. We've never had her tested because it is usually a pretty mild and short-lived thing, but it always seems to coincide with our annual apple picking outing so I know it is seasonal to within a window of just a few weeks. When she was little, either she would get sick right before we went and I would debate cancelling until she begged to still go, or she would get sick right after and I'd think I should have dressed her warmer and not planned as long a day. And this is no different - the variety of apple I like comes in around this time, so we're going picking next week and she's under the weather right now.
It only struck me as possibly being something different this year because several of her schoolmates are dealing with the same thing at the same time, and because we're so much more aware of illnesses right now. Maybe that is just coincidence - her band director, who is the only staff member out sick, just got a diagnosis today of allergies aggravating his COPD (I know his daughter and she let me know because she knew the kids were worried; he's all sorts of high-risk but came out of retirement to start our program this year despite the pandemic), and so did one of the families that went for covid testing - but the number of kids having similar symptoms naturally made me think it is something contagious.