Any pain medicine to have full nerve blocking effect would have to be Rx and runs higher risk of addiction with prolonged usage. No responsible doctor would prescribe such oral pain meds for non surgical procedure in an era where medical community is coming to grips that it has created a generation of addicts where 65,000 people die annually in U.S. alone in an overdose epidemic linked to prescription pain meds usage.
EMLA/LMX topicals are the closest thing you can have access to with pretty good pain control that’s safer. It’s tedious process. You don’t need expensive occlusive like Tegaderm. Glad press n’ seal wrap that has a sticky side works absolutely perfect!