How to deal with prominent veins and menstrual cycle?

FIRST OF ALL: There is no significance and no need to deal. Female hormones dilate blood vessels, veins included. For arteries they have a protective effect explaining why women have less strokes and heart attacks as long as hormone levels are high. So, it is very possible that in ur case the veins u observe are dilated because of the elevated Progesterone levels, hormone of pregnancy.

See vein specialist: Varicose veins tend to worsen during the menstrual cycle due of hormonal changes and fluid retention. Varicose veins are due to underlying malfunctioning (reflux) of the saphenous system. Vaginal and upper thigh veins could be due the saphenous system but could also be part of pelvic conjestion syndrome or even reflux from pelvic veins. You should have a venous evaluation from a vein specialist.