I'm breast feeding and I need dental work done with local anesthetic is it ok?

Yes. The chances of any significant amount of local anesthetic getting into your blood stream, and hence by extension into your breast milk, is minimal.
Yes. Local anesthetic is ok with breast feeding. If you want to be very conservative you could pump and discard several feedings post procedure.
Yes. Local anesthetic during breast feeding is safe and there should not be a problem. If you are concerned you could pump if you wanted.