I don't think she should have been arrested and I think this will come back to haunt him. It was a bad arrest and the city and school will probably end up paying.Unlawful order? No, it wasn't. Arrested her because she hurt his feelings? That's one opinion for sure.
Another is that the situation was spiraling way out of control and that allowing a hysterical girl to keep on screaming risked pushing others over the edge.
I'd feel different if the bystander student was more in control of herself and /or had directly challenged Fields. She wasn't and didn't and he did the right thing by arresting her since the teacher and the AP sure weren't stepping up to take responsibility for anything.
I think he should have just told her to stand aside (not that she was actually in his way as I can see on the film) and just let her get hysterical. She is not responsible for other people as long as she does not actually call for a riot. Anyone else who stepped in to interfere would have been dealt with accordingly. However you do have a legal right to defend yourself and others from police brutality. Now that won't stop you from getting beaten by the cop or arrested but is a legal standard in court.