How long will my breasts be swelled and tender?

After breastfeeding. If you do choose to breastfeed (which is definitely encouraged for your health, baby's health, and low cost!) you will not always have this engorged feeling! feeding immediately relieves the pressure most of the time, and every 2-4 hrs is recommended. You can take Ibuprofen and massage the breasts while breast feeding or pumping. As your baby gets older, you won't notice the full feeling as much.
After breast feeding. Breast engorgement is common when milk first comes in... That is a good sign for most new moms. If you don't want to breast feed, do not express milk. Wear a tight bra and apply ice. You can also take a pain reliever. Without pumping or feeding, no new milk is stimulated, and it should go away after a few days.