Why have the veins on my boobs and areola been more visible and my nipples a dark reddish purplish color and senstive for the last 2-3 weeks?

Periods?: We need some more information: have you skipped or missed any periods? Is there a possibility that you could be pregnant? Are you using any kind of birth control, and if so, what is the name of the method you are using?

I do not know: Hormonal changes for example at ovulation times (or during pregnancy) can change the nipple appearance. If persists, get a check up.