Sounds like you just need to change your action. That's usually the cause the of soreness. Or it just may be a conditioning thing. As we don't know how long you've been playing it's hard to say. Beginners get sore after a bit, especially playing fast, unitl their muscles get used to what they are doing.
It could be that your to tense when you're playing, or maybe making larger strokes than you need to. Hell, it may be the angle you sit to the drums. My advice would be to put up a video so we can see how you play, or go see a music teacher and get them to give you some pointers on how to improve your action.
Making alot of assumptions here, because there could be lots of reasons.
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