Pain in breast

Baby slept for a few hours last night and I woke up in the middle of the night to engorged breast. I felt a ball under my arm so I fed him and massaged it while I did. I feel like my breast is empty and soft but my breast are really painful and I feel a little toughness deep in the tissue. They’re so painful I can’t even touch them. I kept breastfeeding this morning despite the pain and placed warm water/cloth on them but it’s still there. What can I do to relieve them?