My breasts are so full that latching is painful. What should I do?
Engorgement is normal in the first few weeks. Your body makes more milk than needed as a safety mechanism. Latch your baby often and offer the breast any time you are feeling full. This way, your baby will tell your breasts how much milk to make. By steadily feeding on demand during the first 2-4 weeks, your milk supply will regulate itself to provide the amount of milk your baby needs.
Some mothers use pumping to relieve engorgement during this time. A breast pump can come in handy if medically necessary. But pumping too much during these first weeks can damage delicate breast tissue, take time away from latching your baby to feed, and can tell your breasts to make more milk than needed. Though more milk sounds convenient, it can lead to clogged ducts, mastitis, and excessive leaking.
If your baby has trouble latching, a better option is to use hand expression for a few minutes to soften the nipple area. If you decide to pump to relieve engorgement, only pump a few minutes and then try latching rather than fully draining the breast. Cool packs on the breast after feeding can help reduce swelling. Gentle finger massage around the breast can help to drain the breast while your baby is feeding.
SOURCE: https://www.llli.org/breastfeeding-info/engorgement/
https://wicbreastfeeding.fns.usda.gov/engorgement