Can I take cyclobenzaprine for sore arm muscles from working out at the gym?

Rather not. I would rather see you utilize a combination of ice and nsaid medication for muscular soreness after workouts. A muscle relaxant might help you sleep at night if you have a lot of spasm, but i'd stick with the nsaids.
Would not be first. Cyclobenzaprine would not be a medication of first choice. It is really more of a traquilizer and has no direct effect on muscles even though it is advertised to be a muscle relaxant. Rather than resorting to a medication, i would advise a hot shower or bath. If yuor arm muscles are so sore that you need a medication, perhaps you need to back off the intensity a bit.

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