"For no reason" usually describes the absence of an immediate trigger, not the absence of a cause. Crying is a discharge of the nervous system, and the threshold at which it fires drops when the background load is high.
Mechanically: prolonged stress keeps the nervous system activated. In an activated state, the capacity to absorb anything else falls. A trifle — a song, a tone of voice, an advert — becomes the drop that crosses the threshold, and the reaction looks disproportionate because the visible trigger is small, not because the reaction is wrong.
That also explains the relief afterwards. Crying lowers activation; it isn't a loss of control, it's the system discharging.