I would suggest 2 things:
1. don't let him dwell on his feelings when he gets into such a mood - divert and distract to break the spell. You can do this by drawing him into conversations that are so unexpected that his brain jumps from one track on to the next. My DS who cannot sleep because of whirling thoughts gets very frustrated when he tries for hours and still cannot fall asleep. I tell him stories that are funny or weird that he loses track of what was going on in his mind.
2. Please tire him out physically. Take him outside and go walking, biking, trekking etc. When they are physically very active, their moods improve - and preferably to a place far from where there is any team sport activity. Can you find a martial arts class with a demanding instructor who also mentors your son? It is not a team sport and he will get multiple benefits - a thorough work out, self esteem, self control and discipline in both mind and body and overall motor control improvement.

So sorry, I really hope that he feels better soon.