I am editing my post because I activated my story mode habit.... I will restart to the straight answer you wanted:
Simply: say to your doctor you got a cold and it hurts down there. Explain how it hurts, don't worry about that. It's a common symptom, the doctor will simply treat you for infection or for cold. Really in this case you don't need to tell him what you did.
Now here comes the story mode:
I had got a sounding at the hospital and it hurt me for a few days as something new to me. That thing goes way down and I forced removing it when I woke up with it.
Pain passed after. That made me hate any sounding CBT ideas in all my future.
The tissue is very sensitive and the blood is normal when harming it even softly (EDIT: I did insert something small later and got little pink blood, lesson to me how sensitive the tissue is) and the wet environment prevents coagulation for a while (no more than a day I think). If you feel it like an itchy pain just wait and will go away. An infection must really hurt (I didn't have one to tell) so probably it's not your case.
As I understand you didn't cause anything to your urethra but to your dick. Just chill for a couple of days and it will pass. And if you even went too far inside the result is the same: probably an infection, treatment is the same, no harm done.
