You guys aren't terrible parents at all! Growing up one of my sister's had her ears pierced and they were healing fine, then about 2.5-3 months after they got pierced she had left them unchecked for only 3 days and when she checked them again the skin on tye back of her ear grew over one of the earrings. She didn't even realize it was happening and neither did our parents but you guys did the right thing taking her to minor injuries, my parents just took a small knife and cut it out of her ear
Not terrible parents! She was probably playing with them in her sleep.
It can happen and they will heal. In a few years when she is a teenager she might get several piercings that will make you wonder why you were even feeling worried or guilty.
Your a good momma thing happen fast! We can’t control these thing it’s good you were checking on them To begin with! Good mommas care!