That is certainly one possibility, Supermom. You don't say if you have had allergy or asthma problems in the past. There could be many other triggers at school, though, if allergies are at work. These triggers could range from dust to animal dander to insect droppings to mold. Or strong fumes, chemicals in carpeting, paint, cleaning solutions are also well-known irritants to the respiratory system.
I think you will need to do more investigative work to discover what may be going on. Meanwhile, see you doctor to get that cough evaluated!
To your health,
Kathi
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