Chicken missing some feathers?

I have 2 golden laced cochin bantams. They're a couple years old. I got them from a local lady who no longer wanted them because they can be kind of broody (which is something I don't mind). I've had them for a couple months now. One is a little ornery and the other is very friendly. They had a stressful drive from their previous home to mine. When we arrived the friendly hen had a patch of feathers missing on her back near her tail feathers (it happened on the way home - it wasn't there when I put her in the car). I assumed it was because the ornery chicken pecked her and that's what I've continued to believe. I've never actually seen that happen though ornery chicken will try to peck you if you get up in her business.

It doesn't seem to be getting any larger but it's not getting better or smaller either. She could definitely reach this area so she might be doing it to herself. I've looked them both over for bugs and haven't seen anything. I'm worried that it is starting to get infected. It was just skin colored but now it's kind of red. Neither hen has been broody in the past couple months but she just started being broody this week (not sure if that has anything to do with it). Prior to getting broody they were each laying an egg every day or two. I'd get about a dozen eggs per week. She hasn't been laying hardly at all now but I've contributed that to her broodiness (because they started at exactly the same time).

What the heck is going on with her? Is there anything I can do to help her? I can potentially separate them but that would be a big ordeal that I'd prefer to avoid since I've never seen them bother each other.