If I were pregnant and unmarried in Texas, I would definitely meet in person with an experienced and full-time family law attorney BEFORE the baby is born.
Please don't listen to your friends and relatives. They mean well but they often give horrible advice that hurts you in the long run.
What happened in your parent's divorce many years ago is probably wrong today. The Texas Family Code is modified every 2 years by our Texas Legislature and laws change! Texas has become much more father friendly than the laws were many years ago.
I would want to understand what the laws are in the State of Texas regarding parental rights, DNA testing, child support, child visitation (especially for a baby) and what I need to do to protect myself (and my baby).
Unfortunately, many times I get phone calls after the baby is born and after the mother has made many "poor" choices. She listed to her aunt, best friend, mom, or someone she works with -- they are not attorneys and they don't know the law. They want what is best for you. But what is best for you is actually taking the time and money to talk to a real attorney about the judge(s) in your county and how the judge(s) tend to rule in non-married cases.
Basically in Texas, the laws and the judges expect parents to co-parent their child. It does not matter if the dad wanted the mom to have an abortion, if a man shows up to court and is willing to be a part of his child's life, the judge is going to encourage his participation.
In fact, it is PRESUMED joint custody in the State of Texas. With strong facts, this presumption can be overcome but parents need to understand that the laws of Texas (and the judges) want both parents to work together in a peaceful way for their child.
There are these parental decisions called "rights and duties" that are very important. Most people have never heard of them or even thought of them.
Additionally, usually in Texas the judges will order the parent that determines the residence of the child to remain in close proximity to the other parent. So if a baby is born in Harris County normally the judge will order that the parent that wants to be the "primary parent" to remain in Harris county and any county contiguous (touching) to Harris County.
In summary, please talk to an experienced family law attorney BEFORE the baby is born.