Do I need to empty breast?

My LO is 4 days old and breastfeeding well. My boobs are like the size of my head though, and it seems like she never empties one. She'll eat for like 15 mins, 3 times in a row, on one breast and milk is still coming out. I move her to the other one because it's so hard and painful by this time. Do I need to pump out and empty the first breast? Or should I leave her on it? How do you tell a breast is empty?