Recently I joined my school band. My teacher is having me play trumpet, but the mouth piece is sooooo uncomfortable. I struggle a lot to reach the higher notes especially. My teacher told me that all of the instruments are like that, but from how small the trumpet mouth piece is compared to the trombone for example, they can't possible be required to regularly reach as high of notes as trumpet players (within the mouth piece). Should I just keep trying, or switch to an different brass instrument?
This is just from my personal experience, but when I started band (about 7 years ago). I was put on the baritone/euphonium; I think I experienced a similar problem to you where reaching higher notes was almost painful. The next year I switched to the tuba and WOW the mouthpiece was so much more comfortable for me. I think it's easier on instruments with larger mouth pieces like the tuba because the usual higher tuba notes tend to be the lower ones on say the trumpet. I would suggest trying a baritone/euphonium, trombone, or even a tuba (if you don't mind having to carry it home and to concerts).
I agree with Erika and Tim. But also, ultimately, you will need to develop the muscles and technique to reach the higher notes on whatever instrument or whatever mouthpiece you decide to use.
On the lower instruments, like tuba, you often are not required to play the higher notes for that instrument as often, so in some ways it is easier. And often there is more of a need for lower instruments. But whatever you choose, try to make sure to practice at least a little bit every day! With brass instruments you can even practice with just the mouthpiece, or even just buzzing your lips without a mouthpiece. Even this kind of practice, everyday, will eventually help you hit the higher notes.
Yes, some people are better suited to an instrument with a larger mouthpiece, like trombone, baritone horn or even tuba. (And yes, the larger instruments ARE larger and therefore more of a nuisance to carry. You can't have everything easy AND easy in this world!)
Maybe the shape of your teeth really make a trumpet mouthpiece uncomfortable. Or maybe you're trying to get the higher notes by pressing hard rather than by forming a proper embouchure. You can only really sort this out with a teacher.
Anyway, it's over a year since you asked the question. What DID you do? Are you still playing?
I think that larger mouthpieces are going to be more comfortable, on average. My son plays the trombone and doesn't get as fatigued as I do. Of course, with exceptions as you enter more demanding scenarios, the range requirements for lower brass seem to be lower.
However, most kids also start playing trumpet with a Bach 7C mouthpiece, which is very uncomfortable (I heard a unsubstantiated story that it was made uncomfortable, on purpose, so that students would be less likely to adopt a playing technique of using too much lip pressure while playing).
Is your teacher a brass player, or is he a general music teacher? If the later, you might want to consult a more experienced trumpet player for better advise.