Since I am not obligated to support this, does she have a case when she takes me back to court?
This question is oddly phrased since she obviously would be asking the court to modify the existing situation whereby you aren't obligated to pay support. Typically, a change in circumstances will justify a modification in the exsisting custody/visitation/support order, and you have indicated that the circumstances have changed because the child is now living with your ex-wife "full time (not split like [you] did when he was not in [k]indergarten)." It is, therefore, very likely that the court will modify the order and require that you pay support and/or contribute to the cost of after-school care.
Can she amend our agreement and will I have to worry about paying anything?
She cannot amend your agreement unilaterally. However, as noted, she certainly can ask the court to modify the existing order.