X2
Blu Kote should help to hide the redness and "hopefully" discourage picking a little. But space, imho, is your biggest problem.
These sweet girls can become nasty/cranky quickly when cooped up too tightly.
@Chlo's chickens!! giving your general location helps with this question. If you are in the US, then most likely you have cold weather right now - you would want to definitely place her out of the wind and elements. Separating her out
completely would not be a good idea (to me) since integration can be difficult even when weather is favorable and there is plenty of space. Ideally she should be caged/kenneled inside the coop and/or run to heal, unless you have one specific hen that is doing all the picking - then she would go to jail.