Yes, this is exactly the opposite of the conventional wisdom, which is to increase water consumption during a kidney stone attack, for the reasons KarlGauss mentions.
The less water you consume, the higher the concentration of the solutes (salts and minerals, waste products, etc.) in your blood. When the concentration of the solutes in your blood increases, your body makes more antidiuretic hormone. This makes your kidneys put more of the water from the filtered blood back into your bloodstream, and less into your urine. This concentrates the urine with an unusually high level of solutes, including the salts and minerals which most commonly make up kidney stones. This increases the risk of more kidney stones or larger kidney stones, and decreases the frequency of urination, leaving the urine in your bladder longer, which can lead to urinary tract infections.
Drink your water. Your body is always making urine, so “when will it process this water” is really not very possible to answer. The urine is made all the time, from the blood, and the blood is always taking in new water from the digestive system - most of it from the small and large intestines, but some from the mucus membranes of your mouth - your spit turns into your urine, if you trace it far enough.
If you want some gentle symptom relief, I’ve had good luck with cornsilk tea. Cornsilk is the long pale fibers on the corn (Zea mays) cob. You can buy it at an herbalist, or harvest them off supermarket corn and dry them on some paper towels. Make tea with them (about an ounce of dry cornsilk to 1 quart of water just off the boil; cover and steep 15-20 minutes, strain and drink throughout the day.) Marshmallow (Althea officinalis) is another good soothing, demulcent herb often traditionally used for kidney stones, either alone or in conjunction with cornsilk. Marshmallow extracts best in a cold water infusion, but it’s pretty gross that way - it comes out like snot. I usually let the cornsilk infuse for about 10 minutes and then add the marshmallow to the now slightly cooler water and let it go another 10 minutes. You don’t get quite as much snotty mucilage that way, but you still get a good final product.
If that doesn’t do it, ask your doctor about using a urinary antispasmodic medication until it passes. Sometimes that can make it hurt a little less.
Hang in there! This too shall…well, you know…