Dallas County posts their judicial records online so you could search for your case. They are also working to put all the paper filings/order online, so once you have your case number, you can search for the specific order.
If your rights were terminated, you have no obligation to pay support. If they were not, you can be forced to pay support for the time period from when the child was born. There are some defenses, but the burden is on you to prove them. An attorney could lay these options out, but perhaps you should just wait until you get served... nothing you can really do to change the situation at this time.
That said, you should go ahead and find out if an order terminated your rights.
Disclaimer: This answer is intended for informational and educational purposes only and should not be considered legal advice nor forming the attorney-client relationship.
Finding out about termination: I recommend you go the district clerk’s office in the county you believe the suit for termination was filed. There you should be able to find out if you were named a party in a termination suit (having the year and any other information will help). If there was a suit, you can look at the order to see if your rights were terminated. If that trail goes cold, try the Bureau of Vital Statistics.
Can she demand support: Once your parental rights have actually been terminated you are generally no longer liable for future support of the child. I do not know if you had any back child support obligations from before the termination. A judgment for back child support may be an issue.
From the tone of your message, it sounds like you may want to have contact with the child. A word of caution, without parental rights the conservator of the child will call the shots about access to the child. So, even though everything may be great while the mother needs your help, she might later decide to deny you access. You may be setting you and the child up for some heartbreak down the road. This is a general answer, and I cannot give any legal advice without knowing more about the facts and procedural history in the case. This message does not create an attorney-client relationship. For an appointment visit: www.coferlaw.com.