How old is your Cochin? It sounds like your chickie may have a prolapse. Your other chickies will pick at it (because it's red and not normal), hence the missing feathers. Did you feel it? If it's hard, she may have an egg stuck. If you have a stuck egg, I'd lube her bum with some olive oil and soak her bottom in some warm water. If it's soft and pliable, use some Preparation H and gently work it back in place.
I'd bring her in the house and let let her rest in a crate of some kind for the night. The pecking will only get worse. My sister found one of her hens this morning with a similar situation and ended up taking her hen to the vet. The poor hen was distraut and tired and the others had blood on their beaks. Definitley separate her from the others.