Yes,they are synonymous.

"Wound up" might also mean being very tense and full of negative emotion/s. To wind up also means to set the alarm clock by winding it up with a handle...but figuratively it means to make someone tense with bad, negative emotions.

Same meaning = really annoyed/ irritated/ angry/ stressed...

To end up somewhere (or as something) as if by fate or by magic. To wind = to create events by magic, sorcery, witchcraft etc. "Wound up" = past participle from word "to wind up".

I have always understood the expression came from winding up a jack-in-the-box, which at a certain level of tension jumps out of the box. So being wound up (or worked up) means you are stressed at/near the point of exploding or lashing out, snapping at others... losing control of your emotions