First of all, wow and congratulations. A full ride to UT is great!
Regarding Harvard and Yale, you might figure that 85% of applicants are academically qualified to attend. You are very obviously in this group. Quite a few admissions spots are given to athletes, legacy students, and URM students. This leaves you competing with nearly 85% of the applicants for maybe roughly half of the admissions spots. On the other hand, your accomplishments to this point are impressive.
I would be surprised if your chances for admissions are all that different from the overall acceptance rate at Harvard and Yale. I do not know Duke as much (we live way to the north and east of it). I might guess that your chances might be a little bit higher than the acceptance rate, but only a little bit.
Have you run the NPC for Harvard, Yale, and Duke? One thing to think about is that getting a bachelor’s at UT and a master’s at Harvard or Yale or Duke might be less expensive than getting a bachelor’s at Harvard or Yale or Duke, and you will have a master’s degree. When I was a graduate student (master’s degree) at a similarly ranked university there were quite a few students who had done just that – gotten their bachelor’s at an in-state public university (usually one ranked lower than UT Austin) and then went to get a master’s at a top ranked university. Probably at least half of the students had a bit of work experience in between.