Thanks for that information.
You are absolutely right, as a legal parent, you would have parental rights and responsibilities to your child. You will need to be named on the birth certificate as the father and execute an Acknowledgment of Paternity once the baby is born so that you do have legal parental rights to the baby. If you don't do this, and if she is contesting this, you would need to request that the court make a finding of paternity, at which point you can then petition for custody rights.
The rights would include physical such as custody or visitation schedule and decision-making regarding your child, the right to weigh in on medical, educational and religious decisions for example, as well as day to day decisions while the child is in your care.
The responsibilities would be financial such as paying child support if you are the non-custodial parent and she is the custodial parent (meaning the child is primarily residing with her), paying for health insurance and uninsured expenses.
Here is an on-line child support calculator for the state of Texas so that you can input the proper numbers and determine what your child support obligation will likely be.
I hope that this answers your question; if so, please click the green Accept button. Thanks very much and I wish you well here.