I'm looking for a single word that describes a person who often overreacts to things.
You could perhaps try touchy (meaning 1) (American Heritage Dictionary via the Free Dictionary):-
Tending to take offense with slight cause; oversensitive.
or perhaps hysterical (meaning 2) (Random House Dictionary via Dictionary.com):-
or possibly histrionic (meaning 2) (Random House Dictionary via Dictionary.com):-
deliberately affected or self-consciously emotional; overly dramatic, in behavior or speech.
depending on the reason for the overreaction or the exact shade of meaning you are attempting to convey.
If you want only a single word instead of a phrase, then "volatile" (easily provoked, intentionally or accidentally, to strong emotions and behavior) and "hysterical" (tending to react in an extremely emotional way) approximate your intended meaning. Both are generally derogatory and have little/no room for being used playfully, and usually refer as much to emotional states as actions.
Idiomatic phrases and compound words are more commonly used by native speakers to communicate the idea that a person tends to overreact, such as "hair-triggered", "flying off the handle", "high strung", "wound up", "tightly wound", "using a cannon to kill a fly", etc.
I'm not aware of any single word in the English language that simply means "a person who often/usually/always overreacts". Most uses are either more specific or more general, or a person would just say "they tend to overreact".
You could use irascible as a single word option!
irascible adjective 1. quick-tempered: easily provoked to anger or outbursts of temper
2. showing anger: showing or typical of anger an irascible gesture
[Mid-16th century. Via French < Latin irascibilis "quick to anger" < irasci "grow angry" < ira "anger"]