Nipple pain can be normal. As the levels of estrogen and progesterone in the body change (during a woman's cycle), nipple sensitivity can also change. Nipple pain can also be mechanical-- from friction with certain fabrics, for example.
If you feel a firm mass under the nipple, if you see any redness, discharge, or bleeding, or if you have any fevers or chills, it is worth getting checked by a healthcare provider. Women, usually those who are breastfeeding, can get mastitis, which is a type of infection. Others can have inflammatory conditions affecting the breast itself.