TAMU has changed is admissions policy for engineering. You now apply for general engineering with a preference in a specific discipline. You are accepted into general engineering then have to apply to your choice later. So, let’s say you apply for EE and are accepted - you will be shown as general engineering with a preference for EE. You can later apply for anything though - you are not limited to EE.
PetE is ranked #1 in the US and is competitive. I know BioMed Eng. is very competitive. Not sure on any others, but I suspect all engineering majors are very difficult to get accepted into. Your SAT is good, and assuming your class rank is high, then you will have a great shot at any engineering major.