Getting cramps while you run is really common—even seasoned runners get them. Women get them more often than men and, yup, usually on their right side. The reason runners get side stitches more than, say, cyclists, is that they hit the ground with a ton of force, plus the activity involves rotating the shoulders and pelvis in opposite directions, twisting the ab muscles.
MORE: Why Side Stitches, aka Running Cramps, Happen