Hey! Congratulations!
Your baby will be fine, I'm sure. Some women get morning sickness (I did, and it's not pleasant, but my daughter made it worth it all), some women don't.
Anyway, yes, there are many places you can go for care. I live in Minnesota, but I had to go to a free clinic when I first got pregnant with my daughter, because I didn't have any money. After a while, I applied for Medical Assistance. Medical Assistance pays for all pregnancy needs.
I don't know what there is in Texas, but if you go to your county's Department of Human (or Social) Services, then there will be plenty of information about pregnant women and health care. I know that everywhere they have free clinics, though. No need to worry. ^^
If you need help, say so, and I will help you if I can. ^^
With love,
Shayna