What Is Hurt?
Hurt is specific to relationships. It's actually two of the basic emotions mixed together: sadness and anger. We feel hurt when something goes wrong in a relationship. As with all anger, there's an element of blame in it. Hurt is about something that's already happened in a relationship, whereas fear (in relationships) is a hurt projected into the future--"Oh, no, that bad thing is going to happen again!"
How To Tell You're Hurt
You can tell you're hurt when you feel the sensations of sadness (heavy chest, etc.) and anger (tight face, shallow breathing, adrenalin coursing) and when you think thoughts such as, "Why did s/he...."
What's Good About Hurt?
Sounds crazy, I know. What's good about noticing hurt is that once you realize you're hurt, you may be able to share that hurt with the person triggering the hurt, and they'll have a much easier time hearing it than they would hearing straight anger, which tends to evoke lots of defensiveness. "Honey, I felt hurt when you..." feels much more intimate and less attacking than, "You were wrong when you...."
How To Deal With Hurt Well
Hurt's a bit softer than just anger. Trying talking to the person triggering it about your hurt rather than your anger. Subtle difference, but it helps.
Why am I saying "the person triggering it" instead of "the person who hurt you?" Because your hurt is not just about them; it's about both what they did and how you interpreted it. Maybe they treated you wrongly, or maybe you interpreted their actions wrongly, or maybe some of both. We tend to assume, "If I feel hurt you did me wrong!" Okay, often true, but not always. Sometimes you feel hurt because you misunderstood, for example, assuming that your new partner has the same mean intention as your old partner when they do a similar thing. Maybe, but maybe not. To be safe, start the conversation with something more like, "I felt hurt when you..." rather than "You shouldn't have..."
If you feel hurt over and over, it likely means (a) you're in the wrong relationships, (b) you're transferring old hurt from old relationships into new situations, so you overreact, or (c) both of the above.
Hurt's a tough one, but if you pay close attention, you can get better at dealing with it. Try speaking about hurt directly and using the "I felt hurt" technique. I hope it helps.
Wishing you good success with this difficult emotion, Lee
Licensed psychologist, Austin