Hi, many thanks for the query!
You should do- Metabolic work-up to know & to be able to prevent recurrent stone formation. Give 24 hrs urine sample for examination.
For current pain, yes it can be due to another stone fragment.
There is no need for CT, Do USG (KUB), Sr. creatinine
, Sr. Uric acid.
Take anti-spasmodics, pain killers, diuretics with your doctor's opinion.
Wish you a good health.