tmi bleeding

So about 2 months ago I had a URI (Upper Respitory Infection). I was given anti biotic for 7 days. My cough hasn't gotten any better. I am not having to wear bladder pads bc I cough so much I pee myself a lil. Well tonight my wife and I were at the grocery store and I had a coughing fit and tinkled a bit. We get into the car (thankfully) and I peed myself really bad, twice. I get home and shower. I go pee first bc I am still coughing and notice the front of my underwear and the back of my underwear (where the pad wasn't touching) had brownish-redish blood on it amongst the urine wetness. I wipe and there is just a streak of blood. I made sure it wasn't from my hemmroids, I wipe my bottom and there isn't any, I wipe my front again and there isn't blood anymore. No blood in my urine either. Could I be coughing and my body forcing my pee out so much that my pee hole is bleeding...?