I get that if I've been on one side too long I think it's the muscles getting tight. I can't remember the name of the muscles though
I find relief by rolling my sides on a cricket ball or tennis ball - the ouch you get on while doing this is a "good ouch" and it feels soooo much better later.
I need to do this later today as I'm starting to get the pain again and my chiro reminded me to do this. (I used to roll it out on a pilates cyclinder thing when I did pilates classes while pg with DS - the tennis/cricket ball was at home)