If you suspect parasites (mites, fleas, etc.) a few drops of ivermectin 1% (normal cattle injectable stuff) behind the ears on the neck should clear it up. repeat in 2 to 3 weeks to kill off any hatches.
Mites are everywhere unless they are a specific type like ear mites so if the dry skin is from mites you should be able to pull the fur back and see more dry skin. I don't believe there are eye mites. Lots of things kill mites but ivermectin is an easy otc solution. The injectible can be used topically and orally as well. We did it practically monthly when doing guinea pig rescue.
You can also dilute horse paste in water (put it in a sealable container and shake it up really really well so you don't have any uneven lumps) and give orally. That way you only spend $5 for a tube instead of $50 for a bottle of injectible. Also did that all the time with guinea pigs. Use a 250lb dose from the tube with 22ml or cc of water and you get a 1mg/ml solution. Give 1/4th to 1/2 (ivermectin has quite a safe range) of a cc per kg or 2.2lbs. Throw away any leftover solution unless you use something other than water to mix it.