Welfare fraud possibly and it was an honest mistake, what can I do?

My son is 12 years old, he has always lived between my home and my parents home. We've just always let him go between the 2. During school, he is there all 5 days, then with me on the weekends. I get food stamps and medicaid for him, and was just notified today that Im being investigated for fraud because in my situation they dont consider him to be living with me at all. I told them I have custody and he has a room at both places, etc...even that I help my mom with food for when he is there, but they dont care. They said at the least I would have to re-pay everything given for him or they could decide to press charges. Im so scared. How far would they go back? Whats the chance of them pressing charges on me? I never wouldve put him on there or continued to do so had I known its not considered "living with me". What can I do? He said someone would be contacting me within the next few months.