Hi, Ruthy --

The fact that this mom gets headaches only while feeding on one side seems to me to negate the question of it being related to prolactin -- imo, if it was related to prolactin, she would get a headache on both sides.  

I would suggest, since it happens always just on the one side, that it has to do with positionion of her body causing pinching of nerves at the neck, resulting in headaches.  She might like to see a chiropractor, to get aligned, and to learn exercises to help her prevent future insult to those nerves, as well
as finding other positions in which to breastfeed.

Sincerely, Chanita