Can you file Chapter 13 on a court order to pay a percentage of your child's medical bills after a divorce?

In short, No. Debts that do not get discharged in bankruptcy (Chapter 7, or 13) include;
Alimony
Child Support
Criminal Restitution
Student Loans
Debts arising from fraud or theft

The medical bill would most likely be characterized as part of the child support settlement and would not be subject to discharge.