I frequently experience emotions as physical sensations. I can even physically locate them in my body sometimes. For example, I feel tend to feel sadness and sleepiness in my eyes and anger in my forehead.

I get this too, and in fact have long speculated it to be the way that most people probably experience emotions. For example, I feel fear as a ripple through my chest with two distinct parameters. The larger the waves and the more they travel outward from the epicenter, the greater the perceived danger. And the further to the right or left of my chest the center of the splash, the more likely the alleged danger is coming from that side.

I have introspected plenty more where that came from, and have gotten confirmation from plenty of different people that their subjective experience of emotions is similar. This isn't common knowledge, but I assume that's only because of the difficulty of introspecting such fundamental mental facts. Most people have had this sort of mental phenomena on auto-ignore since they were in their single digits, so it's usually quite hard to dig up.

There must be a subjective experience constituting each emotion (or they wouldn't exist), and it generally seems to be a combination between (1) a comfortable or uncomfortable bodily sensation and (2) various other things that would take a while to explain.