If you say you go out for a run after a huge meal that makes you feel like you're about to burst you're probably just exagerating on how much you just ate. It's pretty much impossible to go running with a full stomach without having everything you just ate come rushing back up and all over the pavement.
Once I've eaten till I feel like I'm about to explode though I tend to just sit down and either watch TV, read a book or go on my laptop until the feeling of sickness goes away. Then I'll just carry on my daily routine, which usually involves more eating.