Hi, welcome to the ehealth forum and i am glad to help you.
Your concern is regarding the 6 mm kidney stone having passed on its own and the constant ache still persisting. The stones up to 6 mm can pass spontaneously on their own without any intervention and without any symptoms but the passage usually produces pain and bleeding. Pain can remain in the flank or may shift from loin to groin with the passage of stones into the ureter. Pain usually occurs whenever the stone moves due to ureteral muscle spasm and may stop when it again lodges at a narrow point in the urinary tract.
Opioids are usually required for pain alleviation. Kidney stones may be associated with infection due to obstruction of the urinary tract. A non-contrast helical CT scan is now preferred for localization of stones and hardly misses a stone except very rare stones composed of certain drug residues in the urine. If a stone has passed and constant pain is still persisting, infection of the urinary tract must be ruled out with a complete urine examination and note made of other symptoms like fever with chills, increased frequency of urine, etc. If pain still persists, you might want to consult your physician for a repeat thorough examination and any other associated abdominal pathology.
Hope this helps. Take care.
Note: This post is not to emphasize a final diagnosis as the same cannot be made online and is just to provide medical information and that no treatment suggested above be taken without a face-to-face consultation with a health care professional.