Suddenly extremely sore breasts and purple/red spider veins?

See a doctor: Breast pain can be due to a number of things: cysts, associated with menstrual cycle, superficial thrombophlebitis of veins (mondor's dz). If the pain is persisting, see a general surgeon, breast surgeon for evaluation.

Veins on the breast?: If you mean sore veins just under the surface of the skin of the breasts, it could be mondor's disease, a rare thrombophlebitis of the superficial veins of the breast that causes pain and redness. This is a benign condition that is treated with warm compresses and anti-inflammatory drugs like aleve (naproxen). If it does not get better or if there is a new mass present, though, you should see your doctor.