Welcome to the MedHelp forum!
Kidney stones at times dislodge by themselves and the pain disappears. There are numerous speculations in alternative medicines which say that the stones disappear on medication, but Allopathy does not have any such treatment. Drink plenty of fluids, try apple cider and cranberry juice. These tips may help to flush out the stone if it breaks (but less likely). If you do not want to go for surgery, then you can go for lithotripsy which breaks the stone into small pieces which later pass out in urine. Discuss this with your urologist. In future if you do not want a recurrence then you will need to follow some diet restrictions.
Depending on the stone you have, you will need to avoid certain food items. For oxalate stones you need to restrict (not totally stop) foods which are high in oxalate like beans, legumes, dark green leaves, egg plant, spinach, beets, chocolates and fruit cake. Avoid Vitamin C as its metabolism produces oxalates in the body.
For calcium stones you need to restrict packaged food items rich in sugars and dairy products. For uric acid stones you need to restrict protein intake. Take care!