How do you sign over your rights for a child?

I have a 9 month old girl but the more she gets older the more and more she doesnt look like me. I also want a dna test but I don't know how to go about that. The mother is not exactly what I would concider a good mother she is doing alot of drugs as well as letting everyone else watch the baby but me. She's always trying to cause problems between me and my girlfriend and when I tell her to stop texting me its causing problems she decides to file for child support and throw a hissy fit so to speak. I just want a quiet life with my girlfriend and her to stay outta of it. I would love to help her out if it is my kid but I doubt that. If I sign my rights over will I be done with child support. I'm currently in north carolina.