A side stitch should go away pretty quickly after you stop running or whatever exercise you were doing that caused it. It's generally caused by a muscle spasm, usually of the diaphragm. If it is still hurting a day later, that's probably a sign that it's more than just a simple side stitch. If it doesn't hurt too badly, you could just take it easy for a few days and see if it gets better. If you are in a lot of pain, you should see your doctor.
I have occasionally gotten side stitches on my left, so that's not impossible.
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