I am not on the birth certificate. She doesn't want child support. I think I'm the father but I don't know, and that's bothering me a lot.

Take her to court and ask for visitation. They will ask for a DNA test to be done to determine if you're the legal father. Most likely you will be granted visitation if you're the legal father and she will seek child support.

At this time it would be illegal without the mother involved to do a DNA test on your own as well as it won't hold up in court.