The Sympathetic Nervous System (SNS) and Parasympathetic Nervous System (PSNS) are both part of the autonomic nervous system. Their functions are opposites of each other. Basically, SNS activates systems that you'll need if you ever need to run away from a bear (muscle, bronchodilation, pupillary dilation, increase HR, etc) and shuts down PSNS systems. PSNS activates systems that are primarily associated when you're eating and not doing anything (increase GI motility, secretion, pupillarry constriction, etc) and shuts down SNS.
So, now that's been established you should see why after you eat (PSNS) and then you run (SNS) you're going to shut down the GI and food ends up just sitting in your stomach. Essentially you end up getting cramps as stomach wants to digest but lacks adequate blood flow to do it as most being shunted to active muscles.
Just going by the physiology, you shouldn't run after you eat but walking should be fine. I mean how can you function if you have to do nothing for an hour or so after every meal? Highly inefficient.
. Gratz on getting in!
