According to VetDepot, Neomycin and Polymyxin B are both broad-spectrum antibiotics used commonly in dogs for a number of different infections and conditions caused by bacteria. Neomycin is effective against both gram-negative and gram-positive bacterial, and Polymyxin B kills gram-negative bacteria.
Pet Rescue Rx discusses using neomycin and polymyxin B in combination with a steroid called Dexamethasone to treat eye infections. Additionally, medi-vet states that Neomycin Sulfate alone can be given orally as a tablet or a suspension, topically or put on the eye. Polymyxin B is typically used in conjunction with other medications, most often in topical antibiotic ointments used to prevent infection in superficial cuts and wounds.