the daughter i gave up for adoption is threatening me with legal action [TX] : legaladvice

When I was 14, I was raped by a close family friend. I got pregnant but gave the baby up for adoption when I was 15. I knew the child was adopted by distant family members who lived a state away but I did not know their names or what they were like. We received a sum of 2500 dollars when they took her from the hospital. I do not remember signing anything. I do not know what happened to the friend; I asked to be kept out of the process as much as possible. My mother said he was jailed but I don't know if he's still in jail, how long he was in jail, or if he even went to jail. I have two other children, ages 10 and 7. and am now married. My husband knows about my daughter but has deferred to me on how we should handle the situation.

A month ago, I received a facebook message from a woman who says she is my daughter. I believe she is because her appearance and that she has the same genetic condition as my rapist. She told me that she wanted to get to know me. I spent hours going through her facebook page, trying to decide what to do. I found myself disgusted by her. There are a lot of similarities between her and my rapist as she is rude, vulgar, whiny, and smokes illicit substances. She is married but has a publicly strained relationship with her husband and refers to him by cruel nicknames. I decided that I would not be comfortable meeting her. I blocked her without responding. After a week, I began to receive letters from her. Four letters in total. I did not read those either but recently received a phone call three days ago. I finally answered. I told her that I was not interested in getting to know her and that she should leave me and my family alone or I would get the police involved.

She began to berate me. She told me that my family was her family. She accused me of not going through proper adoption procedures and that I had maliciously sold her to an abusive couple as punishment for being born and that I had held back important information. Without medical records, she lived life as a very sick child and was deeply in debt from the genetic testing necessary to diagnose her illness. She told me that she would be making contact with my family whether I liked it or not. She also said she would subpoena me for her father's name if I did not comply and that I could possibly be jailed for selling a baby. When I began to cry, she offered me an alternative; her genetic condition makes getting pregnant more difficult. If I agreed to pay for a round of IVF, she would consider us "even" and would only try to make contact with her father. Here are my questions:

Does she have a legal right to make contact with my family if I tell her to stay away? Could she force me to disclose information about her birth father? My parents are dead and I do not know how to find out information about the adoption. I did not sign any papers and didn't really speak to lawyers outside the court case. I am worried it is possible my parents merely handed her over in exchange for the money. Could I be arrested for selling her as a teenager? I have money in my savings account and could afford the amount she is asking for. Could I form a contract that would legally force her to leave my family alone if I agreed to pay?

Edit: amount asked for was removed. Also, because several people have asked: I do not want her to know her father's name because the family has previously harassed and threatened mine. It only stopped once I left the state. I am worried that if she finds them, she will give them my address and I will need to move again.