What is the name of the anti inflammatory drug that is administered along with the anesthetic during wisdom teeth removal. I'm not referring to advil (ibuprofen)?

A few. Many times, keterolac, or toradol, is given IV during the procedure. It is a non steroidal antiinflammatory. Also, other steroids such as dexethasone or solumedrol (methylprednisolone) are given as well.
Decadron (dexamethasone) Decadron (dexamethasone) or Dexamethasone is one of the more common medications utilized.
Could be toradol. Each anesthesiologist uses a different combination of medications, but often times toradol is used. Toradol is a very strong NSAID used for post operative discomfort and inflammation.