Regular Skin color but no feathers around the vent

As a new chicken owner i wonder if someone can help me... i have read posts about chickens missing tail feathers and being bright red, but not with normal skin color. My Road Island red is missing a whole patch of feathers around her vent. It is all very swollen and she seems black and blue where feathers have come out. She has also started to loose her balance and list to one side. I have washed the area and kept it clean but it doesn't seem to get better.

I wondered if it was other hens picking at her but i haven't noticed any. She is the only chicken with this problem. But it is the lack of balance that is really bothering! It makes me believe that it is a lot more the mites or other hens picking on her.

If anyone has any advice I would love some!! I will try and get some photos up and so you can see exactly what i mean about the color and the surrounding areas.