
Parasites would be my first thought, these could include, fleas, Rabbit mite or mange mites (sarcoptic or demodectic), even ringworm, depending on where the pup came from, though I would expect to see lesions from the latter two.
Also contact allergy, has he laid on not quite dry floor after you have washed with disinfectant/bleach/floor cleaner. Also air fresheners, especially febreeze and shake n Vac can cause severe reactions.