A paroxysm is a convulsion or sudden fit, brought on because you're freaking out or coming down with something.
Paroxysm is from the Greek word paroxysmos, which basically means "to irritate." If you're irritated to the point of having a wild fit, like if you see someone trying to steal your car, you might go into a paroxysm of rage. When the teacher talked about private parts, the students went into a paroxysm of giggles. A paroxysm can be medical, too, like when an illness suddenly attacks, and you get symptoms like chills and a fever right away.