Do they really said ' You shit yourself' and ' I shit myself' ?

I'm not familiar with the song. But:

It's an idiomatic expression (idiom) not meant literally.

It's meant to indicate someone was overcome with emotion/surprise/fear at some thing, usually in a surprised fashion.

Like if someone were to scare you suddenly as you entered a room, you might say...

"Oh my god I almost shit myself when you walked in".

(The wording comes from the idea that something was so shocking/emotional/scary it made you shit your pants.)

That's the usual usage I've heard it used within.