Limousin hen has raw and red patches on her rump and rear and chest that look like a skin infection. I do not think that it is red mite. Have checked the skin and can see any sign of mites
Welcome to BYC. Can you post a picture or two? She may be getting feather picked by other chickens. Some mites only come out at night, so check her with a torch at night. You can try using some sulfur and pine oil cream (such as Nustock) or menthol ointment (such as sports ointment) to help prevent pecking. Chickens can become cannibalistic if there is over crowding, less than 16% protein in their feed, or are not getting outside to roam. If you can feed a little extra protein in the diet it might help.