@Pelican bird,
As others have said laws vary by state.
However, the one thing that concerns me is that you said this is on school grounds - was school in session? If so, as a parent, why were you there - are you volunteering to help at recess? Just kind of confusing to me.
If this was during school hours, then the school should be in trouble if a child is injured. Biting is a huge no-no even more so than hitting, punching and kicking. There are so many things that can be caught due to the human bite. I would speak with the school authorities about that. Pushing a child away with minimal contact is much less an offense or issue to me than a human bite.
If it was not during school hours and on say a playground where children play - then where was the parent of the other child? Was the child unsupervised? Again you have a leg to stand on as biting is considered an assault and by stopping the other child you were defending against an assault.
Did the bite break the skin? If so, you should definately bring your child to a doctor to be tested. Also how old were the kids - I am guessing they were pretty young - unusual for older children to bite.