Dear Christian:
So different time and place, the very old question. Reading your words, I did remember part of my own experience. When I completed college, I was wondering about what to do with my music, and how to earn money. Then, I started lessons with a major teacher, and enrolled at the Law School. Of course it didn't work out as I planned. The reason you just know: what else can be interesting but music?
So, my dear fellow, do what you already know you have to do. I did it and I have no regrets.
However, this was twelve years ago, and although I'm neither wise nor old, some caution arises... Think about your real perspective of earning your life through the music, and if you figure out a way (or several ones), just go and get it. Maybe your parents will not understand at first, but that's about your life, not theirs.
Perhaps I'm "overoptimistic", but I believe very badly that this need of living music we have inside leads us to solve whatever and just make it work.
Good luck, and best wishes!