"To hurry" means to actually do something quickly or move quickly. It's about your actions.
"To be in a hurry" just means you don't have enough time. It is more about the situation and your feelings.
For example, you are in your car in a traffic jam and you are late to an appointment. You can shout in frustration, "I'm in a hurry!" But you can't shout, "I'm hurrying!" because your car is stuck and you aren't actually moving forward.
Another example: your mom wants you to clean the house before her guests arrive. You are cleaning it but you really don't care. Your mom says, "Come on, they'll be here soon," and you reply, "I'm hurrying!" NOT, "I'm in a hurry" because the focus is on your actions, not your feelings.
Does that help?