what muscles allow you to chew
This is a remarkably common problem, especially among the young. The muscles that allow you to chew (muscles of mastication) can be overworked and strained, the same as any other muscle in your body. If the muscles are well-toned, not weak, and not overworked/strained, this will not be a problem.
Other muscles involved in chewing are the obicularis oris and the zygomaticus. Both are lip muscles. The buccinator holds food in contact with the teeth. All three are innervated by the facial nerve (CN.
BUT, if you chew gum a lot, especially if you have a lot of tension in the muscles of mastication anyways, you're going to have problems... The muscles that make the motion/act of chewing/clenching include the masseter, lateral/medial pterygoids, and the temporalis.