I'm not saying you have only tried the "prime spots", but if you are currently in an area that has any type of private lesson students, more than likely you are not in the one-horse towns all throughout Texas. You have to open your options up a bit or you won't find a job. There are indeed positions open throughout Texas, whether it be elementary or otherwise, but they will be what you make of it. Certainly better than unemployed.
I hope this does not sound snarky as that is not at all what is intended. I know you're going through a tough time. Hopefully you have a strong network to help you through this.