Thanks for sharing your concern.
Chances of needle breakage is very rare,because the instruments are designed very tough and precise to fit snugly in that area.
During instrumentation even if it has happened do not worry, it can be traced by an x ray
of the concerned tooth.you can get an x ray done to rule out needle breakage.
I would suggest that, the reason for pain can be deep penetration of needle into the pterygoid plexus of viens .
For this, you can do warm saline rinse and hot saline compression daily atlest 4 to 5 times.
If the needle is there in your mouth, then you need to consult oral & maxillofacilal surgeon.it can be traced back.
meanwhile you can take muscle relaxants and analgesics.
Hope it helps.