Tobacco smoke is a common trigger. If you smoke, stop now. Get help from your doctor if need be. Avoid places where there is smoke and certainly don't allow it in your home. If your child has asthma, make sure they aren't exposed to smoke at school or at daycare.
Dust mites are tiny, tiny bugs that live in cloth and carpets.
To help avoid them, encase your mattress in a special dust-proof cover. Do the same with your pillow or wash it in water hotter than 130 degrees each week. The water must be that hot to kill the mites. Wash your bedding each week also, in water just as hot. If you can, remove carpets from your bedroom.