In this case, it seems like straining on the toilet — opiate pain killers cause constipation — caused local blood pressure to increase and popped a blood vessel. Thankfully it happened at home, so I could just lay down, apply pressure with the clinic-supplied medical cotton balls and after about 10 minutes it stopped.
Although things were hampered by not knowing exactly where my urethral opening is — things are still so delicate that I’m still not allowed to spread my inner labia for another six weeks. (There’s a risk of tearing or even detaching the inner labia until everything’s healed.) Which means I haven’t had an up close and personal look down there yet. So it was a bit of trial and error, applying the cotton balls and seeing how much blood was on them until I found the bloodiest spot.