It is not unusual for a H.S. senior to have endurance problems above high c.
It is usually from a couple of sources.
1. AIR (you need compression for those high notes)
2. AIR (you need to blow faster air for those high notes)
3. AIR (you are overblowing)
Most people confuse air speed with air mass. If you take in a great deal of air (big breath) it is TOO hard to compress the air and let the speed assist you in the upper register. Your breathing aparatus is overworking due to poor technique and it is a breathing endurance rather than a chop endurance problem. I say this because you describe such a STRONG high c. And a sudden loss of range from high f down to c.
This overblowing is usually caused by….
4. TOO MUCH embouchure tension. There is a mental image of high notes being difficult. And this causes most people to OVERDO the chop setting.
Look in a mirror and play a lip slur from low c to second line g. Could you see your chops set differently?
Now look and play a lip slur from middle c to g on the staff. Could you see a change here? I can’t.
Look in the mirror and play a high c. Stop playing and play a high f or g.
I bet you see yourself really working the chops.
This is completely backwards.
The higher you go the less change is needed. We thought it was hard so we made it hard.
Take a look a guitar. Play an open string and then put your finger in the center and play it again. That 12″ finger movement was 1 octave. If you slide the finger up 6″ you have your next octave. If you slide your finger up 3″ you have the next octave. Notice how each octave has half the movement of the one lower than it. The same thing happens when playing the trumpet.
Each octave requires half of the embouchure change that the one below it needed. 99 out of 100 players don’t realize this and prevent themselves from having a good range. It is this extra tension that causes lots of problems including a poor range and endurance.