I know how you feel. My DS took to biting when new teeth were coming through. I put it down to a bit of feeling confused about the new sensation in the mouth, and also 'chewing habit' (if your LO has been biting teething rings etc all day it's hard to remember not to bite you!)
Also, like you, DS is EBF. When the bite happened, I removed him from the breast and spoke to him firmly to say "no biting" and put him down in his cot or a minute (while hoping that it'd stop hurting soon!) Then when I picked him up again, as he was coming in to the breast I could see the tongue ready to lathing, so fortunately it was ok to feed.
He did it maybe half a dozen times over the course of a couple of months. I suspect that if you try not to react (I.e. squeal/shriek) then it won't become a fun new game/habit to look for the reaction out of mum.
I can't link from my phone but google Kellymom and teething breastfed baby. She offers lots of tips on dealing with this.
Are you giving dd calpol?
Latch will be different if you are using teething gels as they can't feel their gums. So avoid putting on just before feed.
Get some Vaseline or lansinol (sp) for your nips and take painkillers yourself to ease the pain.
This too will pass. It won't last, she's just getting used to it. I used to stop dd and give her a toy to bite (Sophie the giraffe). She soon worked out that Sophie was for chewing and mummy for suckling!