Are there prescription (topical) anaesthetics I can talk to my dentist about

My dentist messed up my bite, so now I have chronic pain in my upper left jaw. I have an appointment on thursday to fix it but I have no faith in him anymore, so it may take a while to fix this problem that I have now. The pain may be with me for weeks.

In the meantime I am not comfortable taking OTC analgesics as I have to take huge doses just to get them to work, i’d use 3-4g a day of acetaminophen or 2g a day of ibuprofin (down from 3g a day) are what I end up taking. I know these are within the ‘safe’ dose but I still don’t like them.

Opioid analgesics work (vicodin, codiene) but they screw up my sleep schedule so I don’t want to use them.

So that seems to only leave topical anaesthetics. Are there any I can talk to him about for this dental pain? I already use 20% benzocaine (aka orajel, anbusol, etc the stuff they sell for dental pain at stores) but that doesn’t work uber well.