Why did my nipple change color after surgery?

In a breast reduction or any other procedure that substantially traumatize is the areola, darkening of color is a component of the inflammatory response is part of healing. Over time, and is many many months, the normal color will return.

The tight vein is most likely Mondor's cord and this will resolve itself with massage.  As to the colour of your nipple, it is possible that your nipple has contracted and thus changed the density of pigment.  Another possible explanation but much less likely is that during surgery the blood flow to a part of the nipple was diminished and that caused the colour change