If i paid for a month on accident, and noticed that my paycheck has been deducting cs payments since the week of 3/11 - 3/16, how do I get my overpayment back from the state of Iowa? Do I need legal Rep to get it back?

If you over paid on child support, you need to talk to an attorney.  There are several situations with differing answers on how to resolve this situation (depending on if Child Support Recovery is involved or not, whether you owe back support or not, perhaps the order also states what happens in this situation, etc). You probably need to have legal representation to determine how to proceed.