I think that you should take the high school classes that are appropriate for you without considering university admissions. Then look for a university that is a good fit for what you have done and for what you want to do. There are a lot of very good universities in the US.
That is a tough combination. It would not surprise me if you end up having to drop one of the two majors. However, dropping one side of a potential double major is quite common.
I have worked in high tech for my entire career, and have known quite a few engineers / software engineers / mathematicians who were also very good at music. Math, engineering, and music seem to go together relatively often. However, most of the people who I know who had this combination of talents had to pick one path or the other to focus on (usually the one that pays better) and got back to the other (usually music) after they were working for a living with evenings and weekends mostly free.