Roof is falling down CHILD SUPPORT?????????

alrighty then here is my situation and question. I had this girlfriend and well we had a son then another then another during all this time we would fight and stuff u know regular problems. Now we decided that it was enough so now i want to give child support seeming how we are not together anymore. But she doesnt want me to because I now foundout that she was getting foodstamp benifits and medicaid she would sell the food stamps and she would tell me she had insurance on the kids shich i paid for but she would just keep the cash thier was really no insurance everytime she went to the doctor she would ask for $50 she was paying the deductable for a doctor visit.. I found out none of that was true she was getting alll benifits using her moms address. Now she tels me i cant go to the child support office because in the eye of the state i owe backed child support seeming that she was claiming i never gave her anything. we were together is this tru or not and what can i do please help