Is my dad right about which Pre-Med school I should go to?

If your high school is non-ranking, then Texas public universities will calculate / assume a rank for you to use in admissions, based on things like previous years’ applicants and your high school’s profile.

https://texadmissions.com/blog/nonranking-high-schools-ut-austin
http://mycatalog.txstate.edu/undergraduate/general-information/admissions/freshman/applicants-non-ranking-schools/