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My name is***** I'm sorry your kitten is having some problems with her eye(s).
Are both eyes affected and what color is the discharge?
Is the kitten otherwise normal?
I cannot tell you to give Tobramycin drops because I have not seen your kitten. But I can send you to this website that shows it is safe for kittens. http://www.vetstreet.com/tobramycin-ophthalmic-rx
The drops will only treat a bacterial infection. If your kitten has a viral infection or if the symptoms are caused by anything other than a bacterial infection, the drops won't help.