Dry air, upper respiratory tract infections, or allergies, or, uh, too much nose picking   are the usual culprits here. To treat a nosebleed, tilt your child's head forward so the blood doesn't run down his throat. This may seem counterintuitive, but leaning forward will reduce the risk of gagging on the blood. Have your child blow his nose to remove any clots, and then pinch it shut with some tissues just below the bony ridge and hold the pressure there for about ten minutes (or as long as you child will allow). Ice can be applied to the bridge of the nose to reduce swelling, if your child will tolerate it.