Breastfeeding hurts so bad!!

I don't know if this is normal but nursing my son is so painful. He's only 5 days old and I don't want to start formula but the pain is so bad I cry. Latching is the worse part but it hurts the whole time he's sucking also. I met with a lactation consultant while in the hospital and she said he was latched fine. She even put him on the breast herself one time and it still hurt. Has this happened to anyone else? How long does the pain last? He's cluster feeding right now too so I can't even get an hour break to let my breasts heal a little.