You’re dad is right. Both my niece and nephew went to UT Austin for undergrad, got into med schools in Texas (UT San Antonio Med School & Baylor College of Medicine in Houston) and matched at top residency programs (nephew at anesthesiology at Wash U St Louis now in his Fellowship there as well, niece is a second year of pediatric residency at NYU Langone, which is number 2 in the nation for peds).
There is absolutely no reason to take on OOS undergrad debt if medical school is your goal. UT and A&M will more than prepare you and their are plenty of amazing med schools in Texas.