Yes tobramycin is safe to use in a cat's eye as long as it is an ophthalmic formulation. If you do not know if the cornea is intact do not use any opthalmic medications with a steroid component.
If the eye does not improve after 1-2 days of treatment have your cat examined by a veterinarian. Ocular foreign bodies cause conjunctivitis that does not resolve with treatment.
If the eye does not improve after 1-2 days of treatment have your cat examined by a veterinarian. Ocular foreign bodies cause conjunctivitis that does not resolve with treatment.