After giving birth the hormonal climate in your body changes and you will usually notice breast/chest fullness at 2-4 days. This fullness usually subsides on its own as long as your baby nurses early and often. Excessive breast/chest fullness is called engorgement. The breasts/chest feel very heavy and uncomfortable, the skin feels tight and can look shiny, and the area around the nipple can be puffy making latching difficult for the baby. Delays in nursing or not feeding often enough or long enough, or trouble latching and removing the milk make engorgement more likely. If you think that you have engorgement or that your baby is not nursing well, be sure to seek help right away.
See links below for more information on engorgement including tips on how to make yourself more comfortable and help your baby latch.
Sore nipples can occur for a few reasons, including if your baby has a poor latch on your nipple. Sore nipples can be extremely painful but there are some things you can do that may help relieve the pain.
See links below for more information on the causes of and treatments for sore nipples and engorgement as well as other information on nursing.