Recently when running I have gotten a cramp or stitch in my right upper quandrant. It isn't bad while running and deep breaths tend to help, but the next day, I am in a good deal of pain. It hurts to take deep breaths or even move around a lot. It even is sore to the touch right under my ribcage. Has anyone else experienced this and if so how did you alleviate the problem.
Pain in the right upper quadrant, which isn't bad while running does not sound like a "running injury". The first thing I would suspect is a visceral medial problem. Start with your primary care physician.
You said you got the cramp when running, but that does not mean it will go away when you stop. As with many muscle cramps, they can continue long after the overexertion that caused them has ceased.
One symptom of overexertion of the diaphragm muscle is pain right under the lower edge of your ribcage. It doesn't matter which side, the hard inhalation of running can send it into a cramp cycle that does not completely relax after exercise. In this case, it will be quite sensitive to the touch in that same spot, and prolonged exhalation relaxes and stretches it out some. Unfortunately, this muscle, like the heart, is one you can't afford to rest too long, so it gets little relief when strained.
Circulation helps muscle tissue heal. You can improve circulation in the diaphragm muscle by reaching under the edge of the rib cage with your fingers and massaging it during prolonged exhalation, with abdomen relaxed, while seated in a comfortable chair. Don't use too much pressure, and do this a few times a day, or whenever it seems to help. Eventually, your diaphragm will strengthen to match the demands of vigorous physical activity, but it may help to lower your exercise intensity (ie: no racing) while the muscle catches up with your ambitions over the next week or two.
Meanwhile, mind your posture. Excess slumping can strain this muscle. Overexertion can come not only from running, but from coughing. If you are running and coughing due to the stimulus of overexertion, that's double-trouble. Again, cut back a bit on your intensity, and look for any causes of coughing that could contribute to diaphragm strain.