Depends on what you mean, doesn't it? But even after we sort that out, the answer may still be that it depends.
A headache is a feeling but not an emotion—at least, not as most people use the word. Anxiety, at least a good deal of the time, is also a feeling rather than an emotion, but it can go either way. A free-floating, undirected anxiety is a feeling. But it doesn't seem too strange to say that anxiety about something specific counts as an emotion.
So maybe we could say that emotions are feelings with objects. At the end of the day, that won't do. Still, it gets at something. We tend to save the word "emotion" for states that are about something, or have some sort of content other than just raw feels. But that's pretty clearly not enough. That slice of apple-rhubarb pie in front of me may fill me with a very focussed feeling of hunger. But that feeling doesn't count as an emotion. What's missing?
The answer, perhaps surprisingly, is reason. Emotions can be justified and they can respond to reasons. If I'm outraged at someone and someone explains the situation to me, the change in my beliefs may well make my outrage evaporate. Sexual arousal seems different. Suppose there's someone whose voice I just find arousing. Reasons and justifications don't have anything to do with it. Hearing those flowing tone and those liquid vowels just does it for me. My feeling has an object, but it still doesn't seem to be an emotion.
So on balance, the best answer may be "feeling" rather than "emotion." But if you want to think more about it, you might look at this piece on emotions in the Stanford Encyclopedia of Philosophy.