There are actually a number of reasons why this is possible. When you run, your stomach bounces around so anything in it also bounces with it. If you have eaten something just before you run, or haven't given yourself enough time to get things started before running, it can leave you feeling very uncomfortable after and sometimes during your running.
You may also want to think carefully about what you might be drinking before or during a run. Everyone reacts differently to physical stress and some people have weak stomachs and some have strong ones. Try to experiment to see if certain things make it worse or better.
If you can't figure it out on your own, and running is really important to you, you can always try and see a doctor that is familiar with athletes or perhaps is a runner themselves to try and give you more specific answers.