How much will it hurt to pass a 3mm kidney stone? How long is the pain going to last?

Stone pain. Even small stone can cause tremendous pain....3mm stone has 70-80% chance of passing without doctor intervention...But still painful..
Ureteroscope. Ureteroscopy is a surgical procedure which can only be performed by a urologist. It is a means of gaining access to the ureteral or to the collecting system of the kidney for the purpose of stone treatment and removal, biopsy or removal of tumors of these areas or for evaluating and treating obstructions of the ureter from sources other than stones.
Ureteral stone. The size of the stone does not correlate well to the intensity of the pain. The nearly unbearable pain of "ureteral colic" is from spasm of the muscular ureter. Although 50% probability to pass on its own within a few days, a 6mm stone sometimes will get stuck and fail to progress. Usually after 5 days, I recommend having the stone extracted with a ureteroscope as an outpatient.
Renal stone. A 2cm stone is not going to pass. Leaving it alone would likely only result in it growing and becoming an even bigger problem than it is now. Unless you know that it is a pure uric acid stone, medication will not help reduce the size of the existing stone. Your two treatment options are shock wave lithotripsy (very likely more than one treatment) or pcnl which is keyhole surgery directly into the kidney with a scope to break up and remove the large stone under direct vision by a urologist.
Paraphimosis. Inability to extend the foreskin back over the head of the penis can result in swelling and literally a "choking" of the blood and lymphatic supply and drainage to and from the head of the penis. If you are unable to resolve this with gentle compression of the end of the penis followed by rolling the skin back to its normal position, you should see a dr promptly as this can cause significant injury to the penis from loss of circulation.
Kidney stones. Medical "expulsive therapy" involves using one or more medications (tamsulisin, ketorolac etc) to dilate and/or relax the ureter, in conjunction with pain control and vigorous oral hydration. The success rate of this approach depends on the size of the stone, your particular ureteral anatomy and your willingness to endure some discomfort in the process.
Ureteral stone. The size of the stone does not correlate well to the intensity of the pain. The nearly unbearable pain of "ureteral colic" is from spasm of the muscular ureter. Although likely to pass on its own within a few days, a 3mm stone sometimes will get stuck and fail to progress. Usually after 5 days, I recommend having the stone extracted with a ureteroscope as an outpatient.
Varies. Depeds on many factors like the diameter of passageways, type & location of stone, amount of water excretion, your pain threshold, etc. Rough stones like oxalate hurt more than phosphate smooth ones. Some hurt for "one second" and hear the stone cling in the commode, others suffer longer. Occasionally, it never passes and never hurts. Drink lots of water and follow with urologist to remove if need.