My question involves paternity law for the State of: Ohio

I have a daughter with my previous girlfriend. The baby is now born and we did the DNA test and I'm the father of this kid.

However, she kept me in the dark durign the whole pregnancy with sporadic emails here and there. I kept trying to make the contact but she simply did not answer me or just ignore me. She will answer me whenever she wanted to answer me.

Long story short, she had prenatal care and she used her insurance to cover most of it. Am I responsable to pay some of that cost? What about the delivery bill or any other services that were used during the delivery? My name is not on the birth certificate because she said that without the DNA test, she will not put me there.

I also want to change my daughter's last name to my lastname, but she does not want to. She filed for child support and I'm willing to pay it. However, all the extra expenses during her prenatal care and after the fact might kill my budget completely. I want to know if I'm 100% responsable or would be something like 50/50 in terms of money.

I created a "shared parenting plan" that way I can see my daughter and we have a guideline when it comes to parenting our daughter. I go and see my daughter every weekend since she was born and now she is about 12 weeks old My reason behind the shared parenting plan is that I dont want her to go out and enroll my daughter or get extra expense such as braces that my daughter does not need because at the end of the day, I will have to pay all of that.

I need some advice. Thanks.