Really bad stitch on right side when running?

Colonic flexure. What you're describing is called a "runner's stitch" altho it can occur during any kind of exercise, particularly high impact. It's due to pressure from a collection of gas where the colon takes a sharp bend under either side of the rib cage. Avoiding eating and drinking carbonated or hot beverage at least 2 hours before exercise may help. "Stitches" aren't serious and resolve quickly at rest.