Resentfulness is the state or quality of being resentful: the fact that someone carries that unfair-angry feeling as a trait, not only for one minute. It is a real noun, but people much more often say resentment. You will meet resentfulness in careful writing more than in chat or everyday talk. Though actually, if a teacher or a book uses it, they are still in the same family of feeling as resentment; they are just naming the quality of the person or the mood, rather than the feeling in one event. In your own sentences, resentment will almost always be the more natural choice.