No, don't give your dog any type of over the counter pain relievers. But there are some medications that people use that can also be used by dogs, Tylenol and Ibuprofen are not safe. They cause a lot of damage to the kidneys and liver of your pet. If your dog has hip pain, there is a medicine called Dasaquin.
Over-the-counter pain relievers are not supposed to be administered to dogs. Though there are some medications which are safe for these animals, Ibuprofen is not one of them since it can damage the dog's liver and kidney.