Been there, done that, got the tee-shirt!

Describe these symptoms to your dentist and ask if you could have anesthetic without epinephrine in it.

The older, non-epinephrine drug was Carbocaine, danged if I know what it is now but my dentist is very well aquainted with it.

Only downside is more shots may be required as the non-epinephrine stuff wears off quicker.

Good luck.