OP, many states have ‘articulation agreements’ or ‘guaranteed transfer,’ whereby with a satisfactory record at a comm college, you can transfer to a U in that state. Many states have this arrangement. I mentioned UC because Vicki brought it up.
You bigger issue is affording the costs in Texas. Google ‘college residency Texas’ or something similar. UT Austin expects a kid to live in Texas a year first or meet some other considerations (work, marriage, etc,) that don’t seem to apply to you.