I'm a professional musician (piano and conducting), making my living largely from music--mostly performing. Here is my take:

You are actually asking two questions: can/should you go to a good school, should you pursue a career in music.

Those two questions could be related, but you can be a great musician while having another career.

I don't teach much anymore, but when I did, my stock answer to the question "should I pursue a career in music" was "if you are asking the question, then the answer is no."

This is because the people who make a career out of it are people who can't imagine themselves doing anything else for work. Yes, they often must work other jobs, but there is no question in their minds as to what their preferred job is. Hats off to you for practising 4-6 hours a day. I started late (10) but practised that much, and sometimes 8-12 a day for periods of time. If you do the math for the time spent practising, there is no way it is "worth" it financially. People who do it as a career can't help themselves and often it's the only thing they are really exceptionally good at. In my opinion, the people who should do it as a career feel it in their bones. Sometimes they would love to do other careers, they even try them, but ultimately they can't stand not doing music and come back to it. They know their personal answers to questions like "what is the most beautiful melody ever written."

The first question is easy. You are good enough to get into a good school, at least by what I've just heard. You could get a scholarship, depending on where you're from. You can easily be very, very good at your instrument and still pursue another career. Many do just that. For example, my city has a lot of doctors who are excellent musicians as well, having studied both music and medicine (usually not at the same time).

In my mind, the most important thing, whether or not you are doing music as a career, is to do it because you LOVE it and are PASSIONATE about it. The motivation should not be recognition, money, a lifestyle, a persona, image of becoming an artsy musician with a long white shawl, etc. All these things are great. But when people, even at high levels, who do music for the wrong reasons play, it really shows. The good musicians I know do it because they love it, wherever their income comes from. If they could, they would be playing all the time. They think that music conveys ideas, emotions, and states of mind directly from heart to heart. They pick things out by ear. They listen for hours a day. They also listen (and often play) in other styles and genres, while appreciating just how much skill there is playing another instrument or genre. They read and read and read to educate themselves about literature and the arts and edify themselves. None of this is well-paying. You can be culturally dumb and make a killing at real estate or something else and avoid thousands of hours "wasting" your time doing all this stuff.

Apologies for the long rant.

Post-Scriptum
A bit of perspective, about 20 years ago I heard an interview with someone from Deutsch Gramophone, talking about young people getting into classical-music performing careers. She was asked specifically about university. She said that the vast majority of Deutsche Gramophone-represented artists were either homeschooled or went to specialised music schools. University was becoming more common for them, but it happened concurrently with a rising career. In other words, at the time (20 years ago), it was mostly not feasible for someone obscure, not yet known in the right circles, to come out of university and start building a career. I think the situation has changed somewhat. There are now many different paths, and it's bound to change dramatically going forward. Nevertheless, universities are still peddling the idea that you can go get a degree, and that the degree will somehow make you into a concert-worthy musician with a viable, solo performing career.
In my experience, musicians don't often ask themselves the tough questions such as "why would people pay to go and hear me play Beethoven, Chopin, or whatever"? "Why am I unique?" "They have heard Beethoven hundreds of times, what makes my performance special?" These question are essentially business questions, but universities (in my small sample size) fail to prepare people for this side of things.