Hi Pianorama,
I went down the music path when I was 18. I majored in piano performance and earned a bachelors, masters, and doctorate in it. No, it was not something I always wanted to do. I made the decision just before leaving for college (or uni as you europeans say). I had played the piano since childhood but not considered it a career option until later.
My plan was to become a college professor. I could not play well by ear or sight read well, but my solo performing abilities were good and teaching interested me. I did not realize ahead of time I'd have to take ear training classes where writing down melodies by ear would be necessary and would be part of my grade. This was stressful and I almost failed out because of it. My poor sight reading abilities meant I had to really limit how much accompanying I took on, and this limited my earning ability as well.
When I finished my doctorate, I got a full time college position, but sight reading and accompanying were a big part of the position, so things just did not work out.
Now I make a living teaching piano lessons to kids. I have about 40 students and I'm getting more all the time. I love teaching a lot of the time, but there are things I don't like about it also -- I work evenings, which hinders my social life. And also, the pay is low, which is stressful for me.
When I was a professor, the pay was very low also, which was much more stressful than I thought it would be. Here in America, accompanists make even less than professors.
I've heard stories of private teachers like me making good money once they get established, so I wonder if that might happen for me in a few years. But here in America, if you don't have a doctorate it's hard to charge a lot for private lessons. So my doctorate helps me get higher rates, but it also has taken 3 and a half years to get a studio that is almost full. So doctorate plus a few years to build your business means I was not supporting myself well until very late in life.
I also know a woman who teaches about 30 private students and does adjunct work at colleges as well as church accompanying, and she has a very nice lifestyle with a house, a beautiful car, and an outstanding grand piano. I wonder if she gets money from her parents though, because I don't know any other musicians who appear to do as well as she does. She is a very hard worker, so if she earns all that money, she deserves it.
But perhaps this will help with your decision: If I would have known the financial realities of making a living in music, I would not have done it. If I were 18 again, I would have reduced my piano practice and made it my hobby, and pursued something else for a living. Financial struggles are just not worth it, and even though I'm "doing my passion," it's not all roses all the time. And having very little money makes life hard in way more ways than you can imagine.
You seem to have a lot of interests. You mentioned math, science, and other things. My advice is this: If music is the only thing in the world that makes you happy, then do it. But if you think you can be happy doing something else, then do something else. Anything else. Because everything pays better than music. And all the practice makes you totally unbalanced -- it's hard to exercise, socialize, and get lots of other stuff done. People who don't have to spend all their time at an instrument have such better life balance.