Hairspray is fine in a carry on, and so is a nebulizer. You can also check a nebulizer, but I would discourage it only because if you have to have it and your checked bag that contains it is lost you are in trouble. For that reason, medical items should always be carried on and not checked. My DS was a premie, with lots of lung problems, and was nebbed everyday for several years, several times each day. If you are bringing prescription medicine to neb, just make sure to carry a copy of it on your person.