I am sorry to tell you but you have no chance at UT engineering. A less competitive major? depends on the major.
As MainLonghorn said, It is just that competitive. And with CAP , you are not guaranteed your major. You are guaranteed you will be admitted to the College of Liberal Arts aka COLA. If you don’t mind a COLA major, then sweet! If you don’t want to be in COLA, then, you will still have to try to transfer in to engineering, which is even more difficult internally. But if that is the way you want to go, research what you need to do to get there if you are offered CAP.
Your SAT needs to be higher by quite a bit to be competitive with your rank and GPA. Can you take a Saturday or after school SAT prep class to help you improve your score before the next test date?
A&M will also be most likely no for engineering. When accepted to A&M engineering, applicants are accepted into General Engineering. At the end of their second semester, they can apply to a major after completing 6 core classes (3 each semester).
I do not see Calculus AB or BC on your AP list. With just pre-cal, I don’t know to what extent that will ding you or not for engineering at A&M. Without Calculus BC, you won’t place well enough on the MPE (Math Placement Exam) to take Math 151 or Physics 218 (at A&M) both core freshman *(and usually first semester) engineering classes. An engineering major only gets two attempts to apply to major. Spring of Freshman year and end of Fall of Sophomore year. It is not “apply as soon as you have the required courses completed”. It is "If your first semester is ___, your first opportunity to apply is X (end of 2nd semester) and second opportunity is X. (end of third semester). If you don’t make it by then, they tell you thanks for playing, bye bye, and you are helped to find a major somewhere. They don’t call engineering Pre-business for nothing.
Also, being out of top 10% and not an academic admit, may lower your prospects,as there are so many top 10%/academic admits applying for majors/engineering, with very competitive stats. While all engineering apps are now holistically reviewed, how well will yours hold up to the top 10%/academic admit applicants?
Maybe shoot for a less competitive major?
You won’t necessarily get a rejection letter from UT or A&M for admissions, as your stats are good but what they will do is offer you a “pathway” to main campus enrollment:
(UT) CAP (Coordinated Admissions Program https://admissions.utexas.edu/enroll/cap) PACE (Path to Admissions Through Co-Enrollement http://studentsuccess.utexas.edu/pace). Read up for program details,
(TAMU) Engineering at Galveston https://engineering.tamu.edu/academics/advisors-procedures/entry-to-a-major/engineering-at-galveston-program, Blinn Engineering Academy https://engineering.tamu.edu/academics/advisors-procedures/entry-to-a-major/engineering-academy-program, or Blinn Team http://blinnteam.tamu.edu/. Read up on program details.
Apply to several schools so you have options. other great schools like UT Dallas, UT Arlington, and many, many others. If you are sold on engineering, get that calculus foundation, and then try to external transfer after your first year or two. Be mindful of what A&M or UT (or wherever you transfer) will accept as tranfer and what courses you need completed before applying to transfer.
