If I had this sort of problem I would use an electrical stimulator like a TENS unit for some relief.
One adhesive electrode patch under the chin, close to the tooth.
A cotton ball saturated with conductive jelly held on the tooth by using a non-conductive piece of something rubbery...something similar to the texture of those rubbery ear plugs. Between the rubbery thingie and the saturated cotton ball I would use a small piece of conductive carbon tens pad material connected to the stimulator.
I’m pretty sure this would provide relief but I have never tried it.
I have all those items here because I once designed FES devices (Functional Electrical Stimulation) and still have large jugs of the blue electrode gel and several models of stimulators. I would use a low-voltage bi-lateral pulse chain with very little time gap between pulse reversals so the nerves would have trouble recovering sensitivity. (no refractory period)
I hope you get to the dentist SOON and get relief!
I am currently researching TENS for a shoulder tendonitis. Nearly all of them say NOT to use on the upper neck, head or face.