Red eye itchy chin

Hello, i have a 8 months old Chin. Got him about 5 6 months ago. A few weeks ago his eye became red then a week after that he started losing hair around his eye. He started scratching more than normal. I took him to the vet she gave me eye drops (ofloxacin ophthalmic .3%) and said otherwise he looks healthy teeth good coat is good. I did the drops for a week but no change his hair did start growing back slowly but his itchyness had gotten worse and eye is still slightly red. So i took him to a different vet who has worked w Chinns...He said continue drops and also gave me tetracaine eye drops to help open his eye. He was slightly closing it vet did say he had a small scratch on his cornea. But he never resolved his itchyness and eye is still not getting better could it be ringworm or does he just have dry skin and should i do a humidifier in his room??...he gets a dust bath once a week...sorry for the long thread Thank you!!