I have sever left breast pain with a large out vain through to my nipple what could it be?

See your doctor: Among other things, it can be a breast tissue infection. If you're breastfeeding, you would also be more likely to have so-called "plugged duct". Potential differential diagnoses are multiple, this could also be a nodule that presses on the vein blocking blood flow and that's why the vein is more visible. It sounds like you should have a clinician examine you.

Mondor's disease: It also could b something like mondor's disease, which is a condition of a painful swollen vein or thrombophlebitis in the breast. Local heat and something like Ibuprofen can help if it is thrombophlebitis. And have a physician examine the problem.