I would suggest talking to the teacher first and getting it worked out and if that doesn't work then go to the administrator. I like what several have said here and offering her alternatives to what she did and how she could have treated it differently, will hopefully be an eye opener on behavior.
It's not just about common courtesy IMO as a adult teacher but hopefully working at a Christian school she should be a Christian and have higher standards on how she deals with others than just the normal person.
She added to the problem by calling him out, she caused him to lose trust with her as well as show other students, it's ok to pick on another student. She might have taken self-worth from him in how she treated the incident. Teachers are suppose to be examples especially a Christian one on how to treat others no matter what they do first or in return. The Golden rule comes to mind too here.
You also need to talk with your son and teach him people even christians can treat you badly and how to act & react to those situations. Scripture tells us to pray for people who treat us wrong and forgive them.
My brother and I first started at a private Christian school before homeschooling and my brother has several physical & other problems and cause of that he went through some humilating times with teachers and students at the school. Teachers & principals will say things sometimes out of frustration and stupidity.
The teacher might think it's was just a minor thing but stuff like that carries over to adulthood for a lot of people unfortunately.
I hope it goes well with your family in this situation and the teacher won't take it badly and do the right thing.
Even at church, I've seen teachers not handle a situation well and caused harm to a person and that's not what being a Christian is about.