I have had half a dozen kidney stones in the last year or so. This definitely sounds like it could be a stone. The pain generally happens as the stone goes into the ureter and travels to the bladder. Once in the bladder, it doesn't usually hurt too much but may cause frequent urination, etc. If you don't have anymore pain, i would just strain your urine for awhile and wait to pass the stone. If you have more pain, you can go to the ER and have a scan done. This will help confirm the diagnosis and rule out other problems.
definetly sounds like a stone. pain is not constant but when it hits its bad. worse at nite for some reason. CT scan is good to show stone position or xray too. urine flow can be comprimised if stone blocks ureter and kidney will swell causing back pain towards side. if left untreated can cause infection. go see a urologist or nephrologist as soon as you can or strain urine at home everytime you pee till pain is completely gone. some stones take forever to pass and others are quick. its good to know what kind of stone you have to try to prevent another. good luck.