Call up your local records office and ask them what the procedure is and how you can get a copy of the forms. I suspect that many of the "requirements" are actually just statistical information, that is, they don't care if you got vit K or whatever, they just want to know how many babies in the state got vit k.
Unfortunately, I've yet to find an online way to do this. I could get you forms to request *copies* of birth certificates in any of the 50 states, but not to get new ones.
ETA: It looks like the Texas Department of Health handles issuing the first certificate. So perhaps start with them.