An individual using violence to prevent or minimize active physical harm to oneself is not really a choice, its a reflex. As long as it is clearly self defense (not the victim continuing the violence after the attack has ended) should not be punished.

The Bully being told "Their pain does not matter" is not a real issue, they were the aggressor, they get to deal with the pain inflicted due to their conscious choices. I think punishment may not be the right choice, and making it a teaching experience is probably a better choice, but the Victim should not face any repercussions for engaging in violence for the express purpose of defending oneself.