A JJ or double J stent
is not known to cause sciatica
either during insertion or during removal. The sciatic nerve
is located quite far away. I am sure you doctor must have done an X-ray before and after removing the stent to be sure that there are no more stones left behind.
Removal of the stent does cause some pain and discomfort but it is only temporary.Developing sciatica is unrelated to kidney
stones. If you problem persists, you should show yourself to an orhtopedician.