Food poisoning without vomiting?

It is uncommon to have food poisoning without the vomiting. It could have been too much of the pizza causing the diarrhea, it could be coincidental that you picked up a GI bug that same day and the symptoms were just appearing after you ate the pizza. No one can know this for sure. Diarrhea is your body's way of getting rid of germs, it usually doesn't last more than 2-3 days. You can probably chalk this up to a GI bug.