I have always been given pain medication when I go in to the hospital with kidney stones. I'm sure they want to be sure you have on first thought. So they will test your blood for urine, and possibly take a ct scan to see if you have one. Otherwise they will want to find out what's causing the pain if it's not a kidney stone.
The doctor told you that you had kidney stones and sent you home without meds? They have always given me the prescription while I was at the hospital or doctors after the diagnoses. If you've been in and seen a doctor, I would call in and speak to the doctor and ask if he can send a prescription to your pharmacy, maybe he just forgot.
When I had my kidney stone attack, I was quite literally in agony. I never thought the human body was capable of feeling that kind of pain and I literally thought I was dying! They shot me up with dilaudid at the ER and then sent me home with dilaudid pills for later. I think I only took 1 or 2 because they're heavy, heavy duty morphine derivatives that knocked me out pretty hard but I needed it because I was in so much pain!
Passing the stone wasn't the painful part. My urologist later told me the pain wasn't due to the movement of the stone, it is due to the stone blocking the urine from being able to move through the system and the backup is what causes the pain. I had no idea until he told me but I guess it makes sense.