I just looked on line at UT Tyler’s program because I do not know anything about it. Mechanical engineering there is ABET accredited, which is good. UT Tyler does not belong to ASEE (American Society of Engineering Education) that gives on line profiles for each college. The profiles will show how many students are in each engineering discipline and also the 75%/25% scores for newly admitted students. Most of the other UT schools are a member of ASEE.
Right now, you shouldn’t limit your choices. Apply to UT, UTD, UT Tyler, A&M, maybe UTA or UH. I do like the schools in the larger cities because it is easier to get internships. Keep your options open, see where you get accepted into the engineering school and wait for the financial information before you make your final decision.