The Texas Birth Index
Ask the librarians at Texas State Library to lookup your name.
The birth information is sorted by last name.
Purchase or, checkout the microfiche indexes from the library.

 
If your name is in the index, your out of luck and it gets harder! (The birth index contain only one of the two possible birth certificates.)

If your name is not in the index then the other birth certificate, the one you are looking for, is. This means that you are fourty hours away. Scan the birth books for the known "Birth Certificate Number". Then get a copy of this birth certificate from the Health Department (not easy, requires stealth.) This will give you the full names and clues to how to find your lost family member.

Note: This works 25% of the time.