4 week old chick with rash/ bald spot

I have two 4 week old chicks (hatched them from eggs and can't tell the sex yet) that were doing just fine until I noticed (yesterday) that one has a bald spot on the back of its neck. I immediately assumed the other was bullying it, but upon further observation that does not seem to be the case. The problem chick is constantly scratching her own neck, so I think she is doing it to herself (and in the last day has made it worse). Interestingly, this chick has been an active preener from the beginning, noticeably more than the other ever was.
I tried looking at the rest of her body, and it looks like she is slightly rashy other places too. They had been in a small feed trough with pine shavings until last week. We moved them to a small hutch (which they did not like) also with pine shavings. I also brought them outside once last week to see how our other 2 grown hens would react to them (from the other side of the fence). Could it have picked up a parasite from outside? I see no visible signs of mites. Any other thoughts? Is there anything I can do to prevent her scratching, and heal her neck?