Talk to any mom with a 2 or 3 month old about breastfeeding and they will tell you one thing. They are worried about their nursling's new teeth. Either I'm the most fortunate woman in the world with ultra sensitive and careful nurslings that never bite or biting is typically not a problem. I have been bitten by accident by a sleeping or startled child. When I cried out in pain they were more distraught than I was. Moms who fear teeth have it all wrong. It's not the teeth. It's the teething they should be worried about!
Nursing a teething infant on demand can make nipples raw. They can turn angry and red and be very irritated. Nursing feels like sandpaper. This happens because the saliva from the teething infant is designed to break down soft tissue, like gums, so that those baby teeth can break through. Unfortunately, that same saliva will also irritate your nipples. The longer the nursing sessions, the more time the saliva has to break down your skin cells. Not a fantastic side effect.
Water and lanolin are the best defense. After every nursing session, rinse off your nipples with plain water, pat dry (carefully!), and apply some lanolin to promote healing. You may be asking yourself, "At what point do I have time to do that exactly?" A teething infant wants to be soothed with nothing shy of a breast. And teething doesn't ever let up until that troublesome tooth breaks through. So when do you have time for preventative maintenance? The same time you use the bathroom, I suppose. Or when you get out of the shower (if you can even manage that). Get creative. Rinse and apply lanolin to one side while the other is soothing baby for a few hours. Then switch.
If you're tandem nursing like I am, there is no hope for you. The teething infant will take up 90% of your waking hours and your older nursling will take up the rest. Your pain tolerance will get a work out. When your older nursling latches on, you may see stars. (I think I passed out a little.) The strong suction of a toddler on a raw, beat up, nipple that has the finest of skin layers eaten away by flesh eating teething saliva is... like sandpaper on a burn. But here's the secret, and you don't have to believe me (I'll understand if you don't). If you stick with the sandpaper on your burning nipples for a few minutes, your toddler will make them feel BETTER. Why? I have no idea. My only guess is the flesh eating saliva is removed from your nipple by the all powerful healing saliva of the older sibling. Nature's way of taking care of the system I guess.