Sounds like you might be getting side stitches, which are caused by eating too soon before a run.  The theory goes like this.  When you start running, your body focuses on fueling your muscles and in the process directs blood flow to those muscles.

In the meantime, if you've had something to eat, your body can't digest the food in your gut without the required blood flow.  So... you get a cramp, also called a side stitch.

Depending on what you've had to eat recently, (some things are harder to digest than others) your body takes at least 2 hours to empty your stomach..  

That's just one of a number of theories as to why we get side stitches, read here for more... http://health.howstuffworks.com/wellness/natural-medicine/home-remedies/home-remedies-for-side-pain.htm

Good luck!

I think the most likely causes are listed above and some also recommend saving fats and proteins until after running and only untilizing the fast-burning carbs prior to reduce the possibility of gas that can also cause side stitches.  Basically, I agree that breathing, diet and running technique are probably all related factors.  There are more compicated theories suggesting pursing of the lips on exhaling, exercises to place pressure on the right side prior to running, trying to exhale on the left foot and so on, but it is a common issue that really has different solutions on an individual basis.  The short answer is that there is stress on the digestive system, diaphram and liver in running, and the good news is the body eventually adjusts (overall in time) to the stress, so try a few changes to see if that helps and otherwise, just remember that your system is adapting to running. 

Hope this helps and best wishes