I had a lower molar pulled and no block was done...
I was able to get it settled down. I got a prescription lidocaine mouthwash that numbed the mouth.
I used a homeopathic remedy that seems to be great for RSD pain flares,
Arsenicum 6x or 30 x several times during the day.

Cranial work on the mouth helped a lot too. The pain tightened everything up, and the cranial work took the pressure off.

It took me about 2-3 months to get it settled down.
Now I know we need 1 block for upper work, and 2 blocks for lower work.

If your dentist won't do the block(s) find another dentist, or an endodontist.
They can do the block on you if you can coordinate to get right over and in the dentist chair, have everyone on stand by for you to be worked on right away.