It could be the size of the reed. What size are you using? I know that 2 and 2 1/2 are easier to get a sound from, and they produce a great tone in the lower register but it's harder to get a clear tone in the higher registers without squeaking. Sizes like 3 and 4 have a better tone in the higher ranges but they require a little more pressure from the lips around the mouthpiece. Experiment with different sizes of reeds and if you find a size that produces the sound you're looking for with the embouchure you use. If that doesn't work, it could be the mouth piece itself. Will your school allow you to use your own mouthpiece? If so, buy one (or two different kinds if you have the money) and try them out with the reeds. I guarantee you'll find a solution one way or another.
Those are just suggestions based on what I've learned from friends and colleagues who play saxophones of all types. I'm a flute player (obviously I don't use a reed on a regular basis), but I am learning clarinet and so I have been experimenting with reeds and a couple of mouthpieces. I've found that an aftermarket plexiglass mouthpiece works fine for what I need, so that's why I suggested it might be the mouthpiece you're using.
Good luck!
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