I totally understand how you feel, toothache is horrible. Have you spoken to your dentist already? He/she should know if the anaesthetics are safe, and will prescribe the right painkillers or antibiotics (amoxicillin is fairly safe to take while breastfeeding. I took it twice).
I had it done whilst breastfeeding. The dentist said, "best to wait til you are finished feeding" and I replied that if this one feeds as long as his brother, it could be another 6 years til I am finished. So he just did it anyway.
I had to have a big filling while I was bfing DD1. My dentist (my Dad, very pro-bf and wanting to keep his gc safe) said that it was fine to do it but my milk might taste a bit funny for the rest of the day. In the end we agreed to leave it but his concerns were for the taste rather than anything dangerous.