and that I can't see my child...as a new father, what are my rights to see my child before going to a custody lawyer?
Criminal Defense Attorney
As a father, you have the duty to support your child and a right to visitation. Custody can be determined based on circumstances and best interests of the child. You will owe child support back to the date of birth, however since you supported the mother and child in your home, you're going to get credit for that. While the juvenile court and child support office will offer free services, if you can hire your own lawyer you should.
Family Law Attorney
Being an unwed father wanting to see the child is tough. Being on the birthcertificate is helpful. I recommend you contact the state and add your name to the putative father registry as well. However, what you simply must do is contact an attorney about filing a petition that will establish paternity, visitation, parenting rights and child support. I handle that sort of case, should you wish to hire an attorney.
Please note that my answering this question, does not, in any way, mean I represent you for this, or any other case. You need to seek that actual face-to-face advice of any attorney in your area who can further explain the law as it applies to your case.