To play from C6 upwards, you don't need to "power" your way through it. Instead, think of a garden hose. The more you cover the end with your thumb, the faster the water comes out. To play that third octave comfortably, you'll need to use a very concise aperture and a lot of fast-moving, concentrated air.
Think about it like this:
The tone hole of the flute splits your air column. Because sound is the way it is, it will split your air column according to the harmonic series. This first division would be to a perfect octave. If your air speed is slow, the flute will physically be unable to split your air column into a higher octave. Faster air = higher frequency = split into the high octave.
Now, the third octave also has it's own special fingerings, so you'll want to make sure those are correct.
To echo others, I would also definitely approach the subject with your teacher to avoid developing improper technique.