Hi Sir or Madam,
Orajel can be used on dogs, but if there is no bleeding, buffered aspirin is a better choice for pain relief. Rubbing the orajel on the gum near the tooth can be more painful than the tooth itself.
Buffered aspirin can be given to a dog with a dosage of up to 5-10 mg per pound every 12 hours. Keep in mind that a dog's body does not metabolize aspirin in the same way as a human and thus should not be given more than a day or two without contacting your Vet. Read side effects and precautions here.
I hope this information is helpful to you.