I found this great explanation of various theories of emotion:
They don’t distinguish between emotions and feelings however.
This article does a great job of explaining the differences with references:
How to Measure Emotions and Feelings (And the Difference Between Them) (imotions.com)
The TLDR; is that emotions are reactions stemming from the amygdala in response to some input. Feelings are how we interpret those emotions or assign meaning to them in the prefrontal cortex.
Emotional responses last about 30-60 seconds in the body (TEDx source Mandy Saligari), feelings can cause the emotional response to get re-triggered.
According to the Gottman research it takes about 20 minutes for your system to recover completely from flooding. (add links)
Emotions we can learn to tolerate, feelings we can learn to change because they are based on our schemas/thoughts/programming/stories we tell ourselves about both the emotion and the stimulus that triggered it.
There is no such thing as a “bad” emotion. Or even negative ones. There are emotions that are unpleasant, uncomfortable, challenging, painful, hard or difficult for sure – and they all serve a purpose. Until you find and act on that, you’ll keep suffering from the emotion. It’s your body’s way of communicating with you. Learn to listen to yourself. Discover your needs. Then share them with others. They have no way of knowing otherwise.
Go watch Pixar’s movie Inside Out if you need help understanding this.