Hey, nice to meet you Ivan!
I hope this goes without saying, but I'm sorry to hear about your situation. I'd like to give you a bit of perspective on the job market for computer scientist in Texas as I am a currently imployed CS major who lives in the state. It's a great place to be in the tech industry as we have had a lot of boom in this feild over the past few years leaving a demanding job market that has fairly stable employment rate. Couple that with the fact that we have lower than average tax rates for the state and overall its a great place to start your work life.
I would suggest you try and decide on moving close to, but not into one of the major tech cities (Austin, Dallas... the list goes on). As for getting the job there are plenty of programming and IT positions around that even a AA degree should be enough to get you in the door as long as you have a personal portfolio of example code you have completed. Also you'll need some form of easily accessible transportation, a personal car is normal but there is always the bus system or even rail ways in some areas.
But essentially, if your going to move anywhere just make sure you run your numbers on cost of living. Though it is easier to live here than in most places you should make sure your expectations for what you'll receive are realistic, for example your not likely to get a town home for $500 a month but you can probably find a confortable apartment that comes with the basics for that price. The added benefit is that there a lot of school in Texas dedicated to Engineering and Maths with a great Computer Science program that local, such the Univeristy of Texas sister schools, that you could like get accepted to and attend for a reasonable price. Out of state at my school on a full course load is approximately $7000 I beleive, which though would be difficult to acqure on an entry level job is not as bad for an entry level tech job. I'm still in school and make above $20 an hour doing web developement so by spending frugally you could save to attend school while working, if you choose to do so (though honestly in the tech industry as with many others experience trumpts education).
I just wanted to try and help you out with what I know about the state you were considering moving to. I hope this helps and good luck.