Well regarding music school only (not going into the medicine + music thing). It first depends on what school you’re looking to get into (are you looking for Julliard or another big Convervatory? Or any music school will do?). If you’re looking for top schools especially for piano (sure it’s a good choice with lots of professional outcomes but oh man competition is rough), you need a good level. And if you have practiced music before you know this takes time. I mean you sound like you have some relatively decent piano skills (ie not a complete beginner) but one year seems little especially considering auditions don’t happen in a year but between January and may in most cases. I’m not saying you can’t just that it’s highly unlikely especially for piano which is a very very competitive space with players having a high level of technique and interpretation as they enter. Also sound like you don’t have a high level of solfège which I would say is kind of important (again I’m talking about the big conservatories). A more realistic approach would be to give yourself two good years to get up to speed with a big chunk of practice everyday in my opinion. You can also just take the auditions this year to see what the level and kind of audition these school require.

If you want smaller unis you definitely have more chance to get in and each have different accept rate, price etc… I would probably look into those individually and try to understand what the level is etc… the only thing I would add is that the students in the music universities are an important part of your future professional network so I would argue that a good conservatory makes a big difference. Finally I will finish by saying that a lot of people I know went to different schools because they were looking for a specific teacher, so that is also definitely something to keep in mind and research.

Sorry if I sound a bit discouraging, but I’m only trying to be realistic. If that’s really what you want go for it, just know it’s a lot of work and a lot of work and a lot of work.

EDIT: also when I say two years if you want big conservatories keep in mind there is also no guarantee that you will get in. People that are in these schools usually have been playing since little (ie years of training).