Is it abnormal for a varicose vein to hurt after giving birth?

No: Many have vv with pregnancy, and superficial or deep venous thrombosis is not uncommon. Pregnancy increases the risk of blood clots, and pain over a vv implies blood clot within, and presents as a cord like area, often with surrounding redness, heat, rubbery/ firm to touch. Suggest that you see your doctor about this, for superficial thrombophlebitis can extend into the deep system in some cases.

Common yes Normal no: A varicose vein that suddenly hurts may well be thrombosed. This is fairly common, but should not be considered normal.

Not uncommon, but...: Not normal. A painful vein after delivery could very well be a sign of thrombophlebitis which is a relatively common complication of pregnancy. As drs. Isobe and w-kl said, let your doctor know about it.

Not unusual: Pregnancy and childbirth put a tremendous amount of stress on the venous system of the legs. This is due to the increased pressure in the pelvis which limits the vein drainage from the legs. I would recommend an evaluation by a vein specialist