Hey hun, sorry you're having this trouble . MR has great suggestions as always .

We went through the same thing when DS was getting his upper front teeth..........it was quite uncomfortable. Giving it time will help.........she will need to get used to feeding with her new teeth. And your areola will get used to the sensation too. In the meantime, you could try changing positions with each feed (as much as you can anyway) just to take the edge off. Lansinoh might not do much, but I know it helped my nipples when they were feeling overly-sensitive, if that makes sense. So if this persists it wouldn't hurt to try a bit (I personally wouldn't worry about it being out of date).

We also went through biting after the top teeth erupted it wasn't fun, but we got through it, with both nipples intact

Hope you both get used to the new teeth soon!!!