Hello,
I transferred from a CC to a "new ivey" this year to major in physics (I had taken linear algebra, differential equations, calc I/II, and calc based physics I/II before transferring).
Also over the summer before transferring I took MIT's Open-Courseware Calc III.
Here is a little bit of background on the preparation I had and the challenges which I faced.
At my new school for my first semester I enrolled in classical mechanics, advanced electromagnetism, general relativity and Fourier analysis / BVP problems (PDE class).
Surprisingly I did not crash and burn, I earned a 3.9 that semester, and a 3.85 in my next taking some even more difficult classes. I felt what prepared me best was having a strong intuition for physics problems (I had read through a lot of the Feynman lectures, and made sure I had a very strong fundamental understanding for mechanics and electromagnetism). My CC worked out of Serway and Jewett's entry level physics book and I made sure I understood nearly every problem in the first 12-13 chapters... Being a physics major you can never know too much physics.
You would be well advised to go through the entry level physics classes on MIT's open courseware to get some preparation for the classes at UT-Austin. I imagine that they have some sort of honors series, so if possible you will want to enroll in that. As far as math goes if you are comfortable with the problems in MIT's multivariable section on opencourse then I would focus more on physics. You will probably be more than prepared to do well in UT-Austin's introductory physics classes so good luck! (As a side note, you did not mention linear algebra, but as far as I am concerned that has been the most helpful branch of mathematics to have a deep understanding of. A lot of the hardest problems I have encountered have been making use of change of basis's and linear transformations, such as solving the equations of a rotating top (which is fundamentally a linear algebra problem!).