If finances are an issue at all, to me it would seem obvious for your brother to stay in-state, and for you to attend a public high school.
If you look at the freshman class at the very top ranked universities, or at any university, there are a lot of students who attended public high schools.
I just looked at the relative ranking of UT Austin and UNC-CH. As @Tarheel2020 mentioned UNC-CH is indeed higher ranked. I do not think that this matters since both are very good universities. However, I do see the reason to go out of state unless finances do not matter at all, which apparently is not the case here. If you were from Texas, I still would not see the reason to go out of state.
Perhaps I agree with @Tarheel2020 and I too am somewhat confused by the question.