My lo did this all the time as a newborn. Sometimes he is trying to stimulate a let down. I have plenty of milk. He just wants it faster. Sometimes he's had enough and needs to burp. Sometimes he's getting too much milk to relax and needs help in another way to fall asleep. He likes laying on my shoulder and being patted. So if he's doing it at the beginning of a session, I'd try breast compressions to get the milk flowing faster. My lo only tugs once or so and makes a little cry and my breasts start flowing now that he's older. He's got them trained pretty well.
Oh and he really disliked my right side until the growth spurt around twelve weeks. Then he started asking for both and now likes to nurse to sleep on that side.
Nursing is definitely not always enjoyable. How old is your lo?