When they are teething, sometimes you can feel a sharp edge of a new tooth on your nipple, but then, you should be also able to feel it with your finger. What works, is changing nursing position, so it doesn't rub the same sore spot on your nipple.
Whether or not your lo is teething or having a growth spurt, this will pass.
Are you sure it is not thrush? Usually teething shouldn't make you so sore, unless the frequency of your nursings has increased a lot.