Tender nipples can be an early sign of pregnancy, and if you have not yet missed a period, it may be too early for a home pregnancy test to detect the pregnancy hormone. Tender breasts can also occur right before periods, especially if you are on birth control pills or take a lot of caffeine. Your tender nipples could also have a very simple and mundane explanation -- friction from rubbing on your clothing.
Certainly if your period is late you should do another pregnancy test. If you get your period and the tender nipples do not go away, even if you decrease caffeine and make sure your clothing is not rubbing, then see your doctor for an evaluation. Tender nipples by themselves are not a sign of anything serious, but any new symptom such as discharge or crusty, red or scabs on the nipple should always be checked out by your own doctor.