I would be very cautious with douching and not recommend it.
If there is anything that is lodged it could make it worse or push if further up.
Douching also destroys the body's natural flora.
If anything, a menstrual period would flush anything out, if it is not lodged into soft tissues.
If you do notice any discharge which is abnormal, then it would indicate that the body is trying to get rid of something and a doctor's assistance would be recommended.
Best wishes.
I would try some good old-fashioned douche - vinegar preferably. If nothing comes out, see a doctor. But douching should remove whatever is in there. It is very unlikely that a stone could make it past the cervix.
You should consult a gynecologis and get removedt, otherwise this may set infection in the vagina
As you are so concerned that some may be stuck in the vagina, I would suggest you see your doctor just to make sure there is nothing caught inside just to be on the safe side.
Best wishes.