You know, you sound a lot like me. Up until I got into AP Calculus I was deadset on going into Biomedical Engineering - then I realized that I really dislike math (engineering-type math), so I was torn between biomed or business. I ended up applying to McCombs and was accepted. I also applied with Plan II as my second choice major, but I'm still waiting on that decision. I'm in the top 1% of my class and in-state also.
If you want to go into Neuroscience, then I would apply to the College of Natural Sciences as a biology major since you'll most likely end up in med school if you go that route.
As for Plan II, double-majoring is highly encouraged, but in certain fields. Like, I doubt a double-major in engineering, especially biomed, would work out well. If I go into Plan II then I'll double-major in accounting or MIS. I'm almost positive I want to go to law school, so a firm Liberal Arts background is great, which is where Plan II comes in. I attended a Liberal Arts Honors class and it is geared toward law - I adored it.
I hope that helped! Feel free to message me anytime you want.