Engorgement is simply when your breasts are overfull with milk. It can cause pain, swelling, heat and in some cases, blockage or infection.
Engorgement occurs most commonly within the first few weeks after birth, when you're milk is 'coming in' and you're establishing a supply-demand rhythm with your baby. it can also occur later in your feeding experience, if you are away from your breastfeeding baby for longer than normal - and not expressing any milk.
The best treatment for engorgement is milk removal, through feeding your baby or expressing with you hands or a breast pump. Particularly in the early days of establishing breastfeeding, feeding every 3 hours at minimum (with one 5 hour break overnight) should help to keep milk moving through your ducts and avoid blockages which can lead to infection.
Engorgement itself can be treated at home with hot or cold compresses, gentle massage, warms baths or showers, hand expressing, pumping and frequent feeding.
If your milk is coming in, focus in feeding on demand with your babies feeding cues, and don't limit time at the breast. Ideally 8-12 feedings every 24 hrs while you're suffering engorgement. Full empty each breast before you switch sides.
Where pain persists, it may be an indication of a blocked duct, or a related infection like mastitis or thrush. If you feel as though you may have an infection, continue following the above advice and see a health professional.