Why am so bloated after running a half marathon?

Hard to say: Depends on a number of things. You may have let yourself dehydrate, and now your body is hanging on to water until things equilibrate. What did you eat beforehand - did you "carbo load" and with high fiber? A marathon his high stress and leads to cortisol release which may cause water retention as well. Whatever it is, it will resolve with time.

Nutrition: Bloating and even abdominal cramping with diarrhea after a long distance run is usually caused by ingesting synthetic nutritional supplements like gu or power gel. If you are using one brand while practicing then use another during the race it can also cause it. Experiment with different nutrition and fluids to find your happy tummy place. The more natural the better.

More info: It is easy to ingest far more fluid that you expend, depending on your pace, weather conditions, hydration level pre-race, efficiency of metabolism, etc. Probably drank too much at all the stops. Should follow your training routine and not drink because it is there, but because you trained for it and the conditions are the same. 13.1 miles does not typically require a huge amount of fluid.