Me and my ex have joint custody with her being the primary.In court it was agreed that I can claim one of the 2 kids on my taxes but it did not get written into our final decree. So do I have any kind of case for claiming my son and file head of household to get the EIC?

No, you need to have a motion to modify the agreement done, you and her sign it, and have it approved by the court.

If the children live more than half the year with your ex, she is considered the custodial parent. Only the custodial parent can claim EIC based on the child and file as head of household with the child as qualifying child. If the custodial parent agrees to let the non-custodial parent claim the child, she would need to give you form 8332. You can then claim the child and get the dependency exemption and child tax credit, but not EIC nor dependent care credit.