Nailed it. End of thread.
No, not end of thread. Just the beginning of a discussion on human nature.
Humans are social animals and this attribute requires that we do as the herd does if we want group cohesion and protection. It allows all individuals within the group to be protected
as long as everyone looks and acts the same. This is why we compare ourselves to others so that we know that we do not stick out.
However, this social comparison is only beneficial when the environment is uncertain or dangerous. In the OPs case, the environment
is uncertain because he's not certain he'll get into a music school. This is why he compares himself to others because if they get in, and he's worse than them, he won't.
The problem is not entirely due to social comparison because it is self-imposed. If, for example, he intended to major in biology instead of music, he wouldn't have this stress since there will no longer be this uncertainty.
Unfortunately for the OP, he's not playing the piano for intrinsic reasons, i.e. pleasure, joy, etc., but for extrinsic ones. He's playing the piano so he'd get accepted into music school. No one likes to be forced to do something they don't want to.