Ah, summer camp. It either brings back fond memories of sing-alongs by the fire and archery lessons with new friends -- or swatting bat-sized mosquitoes and counting the days until you could go home.

This summer, 10 million children will head to camp. For kids with food allergies, asthma, and other health concerns, it’s a time to foster their independence — and for parents to lurch into Worry Overdrive. The good news is, your child is not alone. In fact, according to the New York Times,...