Making Sure I Am The Father

19 years ago the girl I was with had a baby. At the time we both were in our addictions as far as going out a lot to bars and such. When she had the baby I signed the paper in the courts saying that I was the father. We stayed together for about ten years. An order of child support was established and over the next 9 years I got behind on the support, I've in the mean time straightened out my life and cant avoid the arrears. My question is, is it possible for the state of Illinois to do a paternity test after I signed the paper. While I'm in my right mind I want to make sure. If left up to the mother and him, I don't think they would unless court ordered. I want to take care of this, but I also want to be be sure that I'm the father.