You should most likely (if you already haven't) you should see you GP and get some cream loation as the dry skin is most likely causing her some destress and is scratching just like you and I would.
Our DD got the big patch missing on the back of her head and it's from laying on pillows or the floor.
The other thing is she might be allergic to something on or in your carpet, causing irratation and therefore making her scratch or rub at it??
Best of luck