When our range stops at a specific note - there is a mechanical reason why:PRESSURE!
If we are plaing with low(er) pressure and proper body use and breathing, our range just thins out at the top untill it becomes a whisper. there is a point where our support no longer can help keep the lips in motion, but that changes every day depending on sleep, sodium intake, level of playing on the previous day.
Why do we use pressure naturally? Because it works. As we get better, we play smarter and it isn't the six pack in our face or abs that help smart. It is the integration of what we hear, how prepared our body is, how we breathe and the musical content. it is really tough to play smart if we have limited experience and are trying to prove something. It is really tough to get pressure under control if our development is continually "limited" by marching band.
The key to improving the upper register is to find the sources of tension and pressure and intelligently eliminate them. I always teach breathing and body use first. Then comes lipslurs - also as relaxed as possible. Practicing after a hot shower often shows the player how much tension they normally use!
No integration, no success. I recommend talking to your teacher about body use - I have yoga more in mind than athletics. Lipslurs are very key to developing patterns of motion advantageous for the upper register. Getting pressure off of the face goes a long way in unlocking that door at the top of yours.