Clean earrings and other jewelry with rubbing alcohol before inserting them. Wash the area with soap and water. If the redness and swelling don't disappear within a day or two, return to the hydrogen peroxide and antibiotic ointment treatment. See your physician if the infection doesn't clear up within a few days. Otherwise, it could lead to a more generalized infection.
Body piercing with a specialized gun is a quick procedure, but it is painful.
Make sure your child understands what's involved and that newly pierced body parts may be tender for a few days after.