What kind of antibotic can be given to a 9 week old kitten with and eye infection?

The kind your vet prescribes.

Only your vet will be able to help you. Sometimes an eye infection is a symptom of something more serious, so you really should take the baby to the vet.

I like your answer. I just want to point out when a couple of my kittens had eye infections, I used the warm water terry cloth to clean and neosporin under the eye lid. Those infections cleared in about 4 days without adverse affects.