From the Canadian Association of Hospital Dentists, Choosing Wisely Canada and the Institute for Safe Medication Practices Canada:
“FIRST TRY acetaminophen (Tylenol®) and/or ibuprofen (Motrin®, Advil®) or naproxen (Aleve®, Naprosyn®) taken at regular intervals to manage your pain. Talk to your dentist, surgeon or pharmacist to and the right medications for you and to help you with the pain control plan. If you are still in lot of pain, then use the opioid that has been prescribed for you. Opioids reduce pain but will not take away all your pain. Ask about other ways to deal with pain including using ice.”
Regular intervals is sort of like leap-frogging your acetaminophen with your anti-inflammatory. Taking Acetaminophen and 2 hours later taking ibuprofen OR naproxen, and then 2 hours later taking acetaminophen again. This not only helps to prolong pain relief, but the synergistic effects of the two medications together usually provides a more profound pain relief than T3s.
Other things like Keeping Ice on the area periodically, and keeping your head elevated, may also help.
In most cases you will not need an opioid for any dental post-surgical pain.