Try using cotton wool and lukewarm water to clean the nipple.I think this can help soften and reduce the pain.
Yes!!! Mine feel the same way, also when I go outside and it's really really cold out, they hurt so bad that they burn!!!!
Heating pads help, just use low heat. I don't know if yours feel dry, itchy, or started to crack, but mine have been so I started using lanolin and that helps too.