I play the flute and I don’t know if it’s just me but my cheekbones hurt when I play for more the 30 minutes. I don’t know what it could be, I usually have good posture and practice everyday. I have a class (and get graded) for high school band, so it’s really not optional. What do you think it is?
Sometimes band teachers are busier than a one-armed paper hanger. Maybe a short email would help (for instance Dear (name), do you have some time to help me work on my embouchure? I could come in my lunch period or after school on x, y, z days).
I found a similar question, along with a variety of answers, at The Session, a "community website dedicated to Irish traditional music":
All embouchures are unique so it’s not so much that you’re doing something "wrong" it’s more that you’re generating unnecessary tension in your face. For the first couple of months or so, some soreness in the small "kissing" or "smiling" muscles around the mouth is pretty usual but it doesn’t last for very long after you put the flute down. It might be that you’re "grinning" to get your embouchure. While looking in a mirror, you could try experimenting with a more neutral mouth shape i.e. the shape your lips form in repose, and then very gradually shape them until you can produce a note.
Another possibility, though less likely, is that you’re using your cheeks as air pouches. If so, don’t! It’s worth remembering that with a efficient embouchure a flute needs no more air than a whistle.
I would suggest practice for a bit shorter. As soon as it starts to feel painful, quit, but take a note of minutes practiced. And then the next day add on a couple of minutes, maintain that for few days then increase, always keeping an eye on the clock.
The embouchure should be tight in the corners but flexible in the middle. Jaw and tongue should be relaxed.
Try cutting back to 15 min or so as others suggested earlier.
Don’t use your cheeks as bellows; building up the muscles, etc., you may also have to investigate how you are forming the cavity inside your mouth. Your throat should be open, that's to say, you should feel like you’re yawning with your mouth closed. If you’re doing this, your cheeks will also be relaxed although it can be infectious (yawning as I type).
But don’t over do the practice, you can build up your time when the muscles are in a position to cooperate.
The flute goes under your lips, not inside your mouth.