Good news and bad news,
The good news is, if you want a career in music that involves playing and teaching piano, that is certainly possible with very hard work, some luck, a lot of flexibility, and not very high expectations for income. I am a firm believer that most people who are willing to work hard, have talent, and possess a professional attitude can find their musical niche in life, and make a living at it. Why do I believe it? Because I have seen it a happen a lot.
The bad news is, if your goal is to become a concert pianist, the odds weigh heavily in the favor of you setting yourself up for disapointment. The reality is that piano is a very competetive instrument because the world is flooded with piano players.
Someone made the absurd comment that you should go to Juliard or Eastman, as if all you have to do is sign up. The fact is those schools are extremely difficult to get into, and most of the kids who are lucky enough to get accepted have started very young, have huge repertoires, almost no technical problems, and are practically ready to go on tour. Once they get through the program at those schools there is no guarantee that they will become concert pianists, or win competitions - which, sadly, is one of the only ways for young players to get concert engagements these days.
If you are interested in a career in music, think very carefully about what your expectations are in life, how much you love music, what types of work in music you would be willing to do outside of playing concerts (accompanying, private teaching, etc.), and whether you are dedicated to maintain a lifestyle of hard work and little income for the long haul.
If you decide that this is what you want, you should think about what schools you want to apply to. Sure, audition at one or two big names - Juliard, Eastman, NEC - don't waste your time even trying at Curtis, unless the world is beating a path to your door. There are a lot of very good schools that do not have big names. You should look at them, pick a few, and audition there too.
I'm not sure where you are located, but if you are close to a school that interests you, try to make a contact with one or two teachers there on the piano faculty. That is a great way to get your foor in the door.