I agree that a paternity test re the third child is Job One. Because it really sounds like you've become a cash register.
I'd also suggest contacting these agencies and present all of the information to them and I mean ALL of it. Your tax returns. The cost of living in your area. Your most recent utility bills. Rent or mortgage bills, you get the idea. This also includes cancelled checks from paying child support to Baby Mama #1. Gather up the past 6 months and take it with you and GO THERE to talk to someone.
Not on the phone and not online. March down to the office and talk to a human in person, with your copies of all of this information and show them that you're in poverty because of the ruling - and that your two older children might suffer financially.
The agency does not want to starve your older kids. And they don't want to starve you, either, because they want you alive and able-bodied and working and paying so that they don't have to.
I applaud you for wanting to do right by your children, but first determine whether there is an obligation at all to this third child. And if there is, then get some relief from the agency, if you can.