A nipple infection can cause this, but it is also a classic sign of inflammatory breast cancer. Redness, warmth, and pain may be a sign of an infection, the risk of which increases if ever nipples are dried or cracked.
It may be due to duct ectasia (when milk ducts become swollen and clogged), but it could also be a sign of breast cancer (including Paget's disease of the nipple).
Nipple puckering: The one-sided inversion or puckering of a protruding or flat nipple should never be ignored.