Why is the side of my Guinea pig stomach beating on one side?

There could be two things going on here, One he could have an upper respiratory infection. Second since you just got him he might just be afraid and needs some comforting. Go toYou Tube site and view the Towel Trick and hold him in the towel and pet the towel while you hold it over your heart. the sound of your heart is comforting for him and by petting the towel you are petting him through it.

If he calms down in a couple of hours you have nothing to worry about, if not get him to an EXOTIC vet asap.