...well, not really desire, but fantasy. If you do it to someone you like or love (you are always talking about that), it might be the desire to do everything for that person, so giving body parts of myself might be next to dying for a person (which is of course at least a little perveted...).
The cutting would be no fun...I think it would be even more painful and surely more bloody than a ********** (in fact: dangerous...).
Apart from that... it would be a great sacrifice of myself to her. She owns me and my life. With a cut dick, I am her eternal captive. My balls keep my desire, but I cannot release, or only with great difficulty.
I would be humiliated. Peeing would be a minor problem compared to having the sexual desire but no dick to stimulate. Tell the doctor? Well, an accident? Tell a girl? Either tell her, it was an accident, or introduce her to the girl who cut off my dick?
Probably more ashamed, only some kind of proud to "be owned" by the girl who cut me. I would need and keep my balls but it would be a torture and teasing without releasing, too.
Yeah, that would look so vulnerable and cute, somehow...