Soreness on the areola (which is the medical term that doctors use for the nipples) can come from many things. Most commonly, it is from normal activities that we do and some slightly increased irritation or repeated contact. This is because the areola have an increased concentration of nerve ends, making them more sensitive than the surrounding skin and many other parts of your body. It is quite possible that your recent weight lifting is the cause of the soreness, because many common exercises (such as the bench press) cause your shirt to move back and forth over the top of that area, created repeated irritation. While this is an uncomfortable sensation, it should be short lived and not be something that continues to bother you. It would be more concerning if you were noticing lumps or bumps in that region, or any redness or soreness (more than what you would expect from weight lifting, that is). If you have questions or concerns, it is always best to talk to your doctor
who is able to do a physical exam and make sure that there is nothing more serious occurring. Please talk to your doctor if this continues to be a problem.