I usually experience breast tenderness prior to having my period but today the tenderness is accompanied by a burning sensation around the nipple.

Breast pain: Breast tenderness prior to menstruation is not unusual, but the areolar ("nipple") burning could be due to friction secondary to loose support for your breasts after pre-menstrual swelling. If your period was delayed, and pregnancy is possible , get a serum HCG test to be certain about pregnancy. Ask your gyn provider about low dose oral bcp's, if there are no contraindications.