I've passed a couple of kidney stones. It never was a sharp pain as you described. It was more of a dull aching like pain but was really severe. The only time i had a sharp pain was when i went to pee it out and it cut into my you know what. The only way I could get some of the pain to go away without pain pills was to stand on my head, lol. I went to the emergency room on my first one, and actually laid down on the coffee table in the waiting room it hurt so bad. Anyway they took xrays and determined it was kidney stone and gave me a shot of morphine for pain, and wrote me a prescription for hydrocodeine(pain pills). There is a plant that grows native where I live called Queen of the Meadow, and you can boil the roots and drink the water. That has really helped my brother who has about 1 a month, and some other people i know. I'm not sure if you can buy it anywhere, though. There are several minerals and different things that a doctor will reccomend that will help you pass it easier, if that is indeed what you have. If it's too large, I think there is a way that they can bust it up. You should definately get it looked at.
You'll feel like your in heaven when it finally passes into your bladder. Hopefully it is small enough to fit easily through the next little tube and out of your body. My brother had one that got stuck down there and he couldn't urinate it out. He called his doctor and this is no joke what he said... "Go to the store and get a 6 pack of beer and drink as much as you possibly hold without going to bathroom, and then try to urinate again". That's what he did, and he was able to get 3 down. He cranked up the radio and went to bathroom and was able to force it out. It bounced off the toilet and into the floor it came out of there so fast. That thing was huge though. I had no idea something that big could fit through that little opening. it was about 1/4 inch in diameter and spiny looking.
I'm not reccomending the beer thing cuz it sounds crazy to me, but you do need to see a kidney specialist and let him take a look. Good luck!