My cat has received all her shots. We recently introduced a new kitten. The kitten had discharge from her eye, but it went away. Now my cat had green and black discharge coming out of only her left eye. She's squinting it like it hurts her or something. We don't know what's wrong. We keep wiping the discharge out but it doesn't stop.
Sounds like an infection of some sort. I would take to vet if it doesn’t clear up, like, real soon. Yes cat's can have or develop allergies, but this doesn't sound like an allergy.
It could be an allergy but it sounds more like an infection. If something is irritating the eye it would cause the discharge and if the discharge didn't remove the irritant then it could rub the eye until it causes an infection. Constant irritation can cause blindness so you should talk to your vet.
I've never heard of cats being allergic to each other.