Remedy for sharp urethral pain?

I am currently passing a kidney stone as dozens of tiny fragments. I just tested negative for a UTI on both dipstick and culture. I have no discomfort when actually urinating, and no other symptoms of a UTI. No redness in the area.

Through the day I get a very sharp pain in my urethral opening. The pain is worse at night. I suspect it is physical irritation from constantly passing urine and scratches from all the fragments.

Is there anything I can use to ease this pain? Rinsing with very cold water brings temporary relief, and this isn’t the most practical technique for throughout the day.