Anyone know what this is?! -Skin

Hi. I work in a daycare and I also play sports. After a practice I noticed that my leg underneath my knee was pretty scratched up (normal, happens w the sport). A few days later I noticed that the scratches and cuts I had sort of faded but I was left with this round,

brush burn looking thing. I didn’t think much of it, but when I went to work, I noticed a toddler had a similar looking round rash on her arm!!!

I have had this before but the doctors dismissed it as a patch of dry skin. Any ideas? It’s weird that the child and I have the same one right ??