You are auto admit UT Austin, although Cockrell is separate, but I think your chances are pretty good. Get in your app early.
With UTA as a “floor”, I’d limit your total apps to just 6-8 reaches, especially ones with generous FA. Unless your family has a lot of assets, some of the privates like HYPMS will likely be cheaper than OOS publics. The quality of your essays matter for schools like these, so avoid cookie cutter essays in order to apply to a bunch.
No guaranties in admission to your reaches, but you have a decent shot as long as you don’t fall into the trap of treating admissions like a lottery and don’t customize each app.