I do believe at UT Austin, if you don’t get your first or second choice major, then you are asked to choose a major that is open at the end of the admission cycle. It is a difficult process because all students that don’t have a major are given access to all open slots at the same time. Its like hitting the lottery. Math will be a difficult major to get because many students who can’t get into CS go for math. General studies, education and COLA seem to always be open.
As a safety school, A&M engineering is also a reach but you would have a better chance there. UT Tyler, I don’t know about. I do know both UT Dallas and UT Arlington have well respected engineering programs as well as Texas Tech.