You said you received papers about a child support review. This sounds like there was a child support order already from a court concerning your daughter. Yet you also mentioned a paper asking you to admit paternity and waive the DNA testing (genetic testing). That does not make sense to me. If there was a child support order issued by the court and signed by a judge, that is the amount that they will say that you owe. If you paid the mother or your child directly, those payments would be considered a gift. You can go to court with proof of all of the money you paid and ask the judge to give you credit for those payments. Sometimes that will work. But, if you have lately been just buying things for your daughter as she needs them, the court will mostly likely not give you credit for that money. Child support is supposed to cover part of the food, shelter costs, and other things that a parent has to pay. If you are buying clothes and shoes, that's fine, but that is not considered child support.
If no support has yet been ordered, because paternity has not been established, then you will not owe any support for years past, but only from the recent filing of the request. This would not add up to $10,000 or more. This would just be possibly a month or two of support owed.
I realize you don't have a lot of money, but I really think you need to hire an attorney to review your situation with you. It is very hard for me to determine without examining your documents, exactly what is going on. In any case, gather up the documentation of what you did pay, and get it ready for court. You might also want to take a witness that would testify how much you supported both of your children.
I hope this helps you. And please, consider consulting an attorney, rather than go into this yourself. Good luck.