Misty, we pierced our dd’s ears twice. They never became infected the way you’re describing, but the holes stretched out over time, and we were afraid it was going to tear through her ear lobes. It was especially worse on the right side. We don’t know if she was playing with them at night and stretching them out, but it’s possible. I regret having them pierced at all. The first time was my decision; the second time was because she wanted them. I wish I had waited until she wanted them rather than going through it twice and still not having earrings. The stretched holes have not healed, although we have never tried to put an earring back through them. We probably won’t ever try again.
Similarly, I had my nose pierced twice (I know, I know, not typical for a homeschooling momma). The first time I had to take it out because we moved so my dh could attend Bible college, and it was against campus rules to have piercings other than ears for women. (We personally do not have any reasons why piercings are unbiblical, but this school was very conservative and Pentecostal in nature, and we desired to follow the rules.) As soon as he graduated and we moved off campus, I re-pierced my nose. I actually loved having that small speck of sparkle on the right side of my nose. The piercing did fine until it had been in for nearly a year. Then I started getting what appeared to be a large pimple right around the piercing. Despite cleaning it and keeping make up away from it, that pimple came and went for over a month. It was painful too. One day while taking a shower, I had had enough and yanked it out. Within 24 hours the hole was completely grown in, the pimple was healed, and I decided that it was time for me to outgrow my nose piercing. 
All that to say that with piercings, it’s totally possible to do everything right and still have to take them out. I’m sorry for your dd. She did earn it, and perhaps you can reward her with something else that makes her feel big and special.
Blessings,
Lindsey