Nebraska has a state law mandating every school to have an emergency kit containing adult and child epi-pens, a nebulizer, albuterol in saline and a few other items. The school must have a protocol signed by a local physician directing the use of this kit in the event of a presumed severe asthma attack or anaphylactic reaction.
So, yes, every school has a nebulizer. But it is to be used only when the emergency protocol is implemented.
Children with routine or prn orders for a nebulizer must bring their own from home, along with tubing and meds.