When a firework explodes 100 feet away I can see, then hear and then fell it.
I can explain the sight and the sound.
What happens to make me feel it?

What you "feel" is called percussion. Its from the rapid expansion of air surrounding the explosive device. Sight ( speed of light ) is faster the sound ( speed of sound ) then comes percussion ( slowest ) .

You have p and s waves in an explosion. Your p (Primary) waves are compression based, and thus form sound. They are just minor disturbances traveling very fast. The s (Secondary) wave is just a difference in air pressures, like wind.