Pay attention to the material it's made of. Sometimes, skin can be sensitive to different things. My little sister can't wear gold or gold played earrings, but does just fine with the cheap-o type. My daughter can only wear sterling silver earrings. Anything else irritates her. So I would see what her piercing earrings are made of, and buy more of the same material. If they work, great! You know she is reacting to the material. If they don't, I'm not sure what else to do.
As for squeezing it on too tight, I would get some of the earring back with the caps, so they can't go too tight. (I know they sell them at Claire's Accessories... And it's probably a safe bet that you could find some at Walmart.)