Engorgement can lead to sore, painful breasts or a breast infection. So it's best to try to avoid it. The longer you wait to breastfeed or pump, the more uncomfortable and engorged your breasts may get. If you can't feed your baby right away, use warm compresses and try to pump or manually express your milk. Also follow these techniques these Apply an over-the-counter breastfeeding ointment such as Lanolin. ... Apply cold compresses to help with soreness from engorged breasts 5 Consider using over-the-counter soothing packs, such as Lansinoh Soothies. Let your nipples air out after feedings.