I have a cat with a horrible eye infection from an unknown cause. My vet said it shouldn't be contagious but she isn't 100% sure. I've been keeping my hands and body clean after giving the cat her medicine/messing with her, but is there any chance he can catch the infection? I have another cat who wanders the house and spends some of her time in the bedroom. He sleeps in a closet in his cage and she isn't allowed in there, but he plays in the bedroom. Thank you!