Jia you rach and fish!!
When breast engorged and very painful even to touch, then use cold compress. If only engorge and hard, but not extremely painful, then use hot compress an d massage.
If nipple painful, it's different la, tat one need to apply nipple cream and rest the breast by pumping instead of latching. Also latch whenever possible, 5 min or so to season the nipple for latching. If latch correctly, only the the initial latch on is painful, once the bb starts sucking,should be ok.