The only OTC pain reliever that is safe for your dog is aspirin. Only your vet can tell you how much is safe to give your dog. Never simply give your dog an aspirin pill because it may be way too much.
NEVER give your dog NSAID pain relievers like Ibuprofen, Naproxen, Tylenol (acetaminophen), or opiates for pain. Some websites say you can give these, but they can cause irreversible kidney and liver damage.
ALWAYS call the veterinarian to ask if something is safe before giving it to your dog, including topical rubs, creams, and pills.
Just because a pain reliever is safe and effective for you doesn't mean it's safe for your furry best friend. Many dog owners have accidentally poisoned their dogs by using human products on them.
CBD oil is anecdotally effective for pain relief, but it can cause serious damage if given in too high of a concentration. Only use a formula that is made for dogs, and available at a pet store.
There are highly effective prescription pain medications that are safe for your dog. Your vet will give you appropriate pain medications for your dog at the correct dosage if it's needed after the dental visit.
If your dog can't get in for an appointment right away, the vet may prescribe pain medication at the correct dose that you can pick up from the pharmacy to safely treat your dog's pain while you wait.