My immediate thought was as Twizzel, red mite in the coop. If that is the case they will have spread them to the shed, because not all the mites leave their host before morning. The usual place are the the joints between the perches and the walls.
Most effective treatment is a fine jet steam cleaner, repeated until you no longer find them under the perch. Paint the ends of the perch (and only the ends where the chickens can't touch it) with creosote, so the mite can't get past it and back to the coop. They will climb the walls and drop onto the chickens at night and then be trapped on the perch in the morning.
We were constantly having problems in our coops until we adopted the above method, because no other treatments are 100% effective. No red mite now for 8 years.
As said, it could also be far too hot in there because of insufficient ventilation. Rats are also a possibility, but they shouldn't be able to get in at night.