Runners trots is very common, but I'd be very concerned about the bloody diarrhea. Definitely get that checked out to make sure there is no pathology there. Also, make sure to eat lots of yogurt or take probiotics once you're done with the course of antibiotics to rebalance your body's flora.

If it turns out to be that you just always get bloody diarrhea as a result of running... well, I'm not sure how much it's worth to you to do that kind of exercise. KWIM?