Getting in over your head can be a good thing, but it depends on how over your head you are.
I wasn't an especially good HS saxophone player, at least in retrospect. I was the best in my high school, but I went to a private school and my band only had about 30 members and that was grades 7-12. My parents didn't give me a choice of where to go to school initially, I had to start off at the University of Houston. I went there for a few semesters, played in the marching band and basketball band, but failed the audition into the school of music and was never an actual music major there. I went to a local community college with a good reputation for music, got good instruction from some monster players, started studying jazz, and improved a lot in two years.
When it came time to transfer back to a 4 year university, I still intended to be Music Ed, but I wanted some place with a jazz program/degree. That pretty much left UNT, Texas, and Texas State. From where I was at that point, I don't think I would've done well at UNT. I think I would've gotten buried. There's what, 120 saxophone players there? To big of a pond for me. UT has a really good program, though smaller (almost every program is smaller compared to UNT), but at the time they were kind of overcrowded. So I opted for Texas State. It was a good situation for me. Fairly big program (4th largest music school in the state after UNT, UT, and UH). I was able to step in, not be buried but have people above me to aspire to and people on my level to push me. So with the jazz bands there, I spent one semester as lead alto in the 3rd band, one semester as 2nd tenor in the 2nd band and then 2 years in the top band, one semester as 2nd alto and the rest as lead. It allowed a nice progression. Maybe I could've dealt with a bigger pond and more competition, but I don't know how much bigger. I still don't think I couldn't handled UNT at that time.
So I really think it's about knowing yourself and what environment you're likely to succeed in. There's a player on here, James Barger, who goes to West Texas A&M (?). Not the first school you think of when thinking of music schools in Texas, but he's a great classical saxophonist. He's been able to succeed in what I assume is a smaller environment.
Go to the different music department websites and find out what their audition requirements are. If you haven't already, start working on the music you'll use for your audition. Auditions usually take place from November - February/March. So you've got a year, give or take a few months.
Also, don't go to the University of Houston. I like UH, I support their athletic teams, but the Moores School of Music is run really poorly. When I was there, I was allowed to take theory classes. After I took theory elsewhere, I realized that the way they teach it there is a joke. The book, that their faculty wrote, is abnormally thin and they rush into things and don't explain it well. They had us trying to do 4 part harmony in the 2nd week of school and didn't have a clue about what I was supposed to be doing. Last year I tried to go back to take some post graduate courses but trying to get anything done was a nightmare. It was a nightmare. Nobody knew what the hell they were doing and I couldn't even through the application without jumping through a million needless hoops. Again, it was a joke. I ended up not taking any classes there. A lot of the graduates that I know don't speak highly of the program either. They went there because UH threw scholarship money at therm, not because they had a high opinion of the program. Do yourself a favor and cross them off the list.
That said, I've known people who've gone to UT, UNT, UT-Arlington, Baylor, TCU, Texas Tech, Stephen F. Austin, Sam Houston, UTEP and UTSA and they all seem like viable options.