Firstly you should wash out your dog’s nose and eyes with cool water thoroughly. If the skunk smell is still present, take your dog to the veterinarian for further treatment. You can also try using hydrogen peroxide in a squirt bottle to clean out your dog’s nose and eyes if they are still red or irritated after the water rinse. You may also use an eyewash solution that is available at the drug store (available without a prescription). This solution helps wash out any residue of the skunk spray that may have gotten into your dog’s eyes or mouth.