i would take her to the vet without giving her anything. while generally the stuff they prescribe for eyes is not specifically for chinchillas, you don't know what is wrong with her eye, it could be something completely different to what your cat had and so you could make it worse.
it's possible she damaged it with hay (my guinea pig did that, several times!) in which case the vet will be able to tell if there's any damage to the eye using a special dye. it's possible it's an eye infection, respiratory infection or a tooth problem. if it is a respiratory infection, you would want to get her seen fairly swiftly.
if you want to do something for her eye while waiting to see a vet, you could gently wipe her eye with cotton wool pad or ball moistened with salt solution (boil water, mix with salt, let it cool down - i usually use it when it's still a little warm rather than cold) - this will clean off the discharge and if there is eye infection present, it could help a little.
in any case, you want to see a vet before putting any goo in, especially as it had been prescribed for a different animal, of a different species.
