Sucks to hear that, OP. Sounds like you're handling it good, and hope your girl's cut heals fine.
Cut up half of my eyebrow as a kid once. After we came back from getting it glued shut at the doctor's, my parents went back to work and I can't remember even paying attention to it. Kids get cuts and bruises all the time, you're the one to teach her how to handle it.
VU for being a good parent for your kids.