Oh man...lol. I know how you feel - yes it's "normal" in the sense I think a good amount of people experience this but it's mostly due to fueling/hydration.
I think it's much more common in distances that are 10k and higher - mainly for the reason you are questioning (hydration).
When you are running, your blood flow is directed toward your larger muscles in your legs (and some upper body) that is doing most of the work. So organs like your intestines/bladder/etc are receiving lower amounts of blood flow and oxygen during that time period. The less hydrated you are the more uncomfortable it will be towards the end of the race and DEFINITELY afterwards. Depending upon how dehydrated you are, it could progressively get worse for a few hours before it dies down. When I was in college I use to dread the 10k because if I wasn't careful about what I ate and drank, I would get what I referred to as "10k tummy" and I would be laying in the fetal position in my hotel bed later that night moaning and having cold sweats because it felt like I had to go to the bathroom for the millionth time (but couldn't). Sometimes it would be so bad I couldn't finish my cool down because the onset of cramps would start and I'd have to go to the bathroom. It also made me very light headed. On one extreme instance (after a marathon workout) I actually got sick about 2 hours after my workout. Leading up to that point I had experienced bad stomach cramps/nausea and wasn't really able to go to the bathroom that much. I couldn't really keep water down because my stomach was so sensitive at that point from having no hydration and going a long period of time (1:45mins) with low blood flow during my workout.
It will get better, but I would try to sip on something with a little bit of electrolytes/sodium. See if you can stomach some warm chicken broth and eat some saltenes. That usually ended up helping me in the end. Also, it MIGHT help to apply a little bit of heat at the same time to your lower abdomen (stimulate a bit of bloodflow to the area).