My question involves paternity law for the State of: Texas

My 18-year-old son is a senior in high school. He was recently involved one night with 22-year-old college student. Now, she is accusing him to be responsible for her pregnancy even though she has openly admitted to having been with other men during the same time period. She has even stated openly that she had her monthly cycle after this particular night.

She is continually harassing my son with legal threats regarding child support and medical expenses through voice mails, text messages, and emails.

Is there a way to stop her harassing messages? Nothing can be done to prove his paternity until after the child is born anyway, correct? She would have to initiate the court ordered paternity test if he denies he is the father, correct?

Thank you for your time and advice.