Back pain over ilium (very few patients know the name of the bone) so i am very much impressed with the knowledge you have of anatomy.
Well you need to provide me with information as to when you started getting the pain and what caused it...did you overexert your self or did you lift anything... so far we can rule out any renal component as if you any stone problem the pain would had been persistant and not only on bending.
This could clearly be a case of SACRO ILIAC JOINT DYSFUNCTION. The SIJ though immovable, does move few mm if muscles around it are tight. It could move upward / downward/ rotate inside or rotate outside & we call it upslip / downslip / inflare & outflare of iluim respectfully & the classic sympom would be one sided pain especially on bending / turning on the bed /getting down from car etc. Only an experienced Physiotherapist who is trained in manual therapy in India are the only ones who can set this issue or any chiropractic or osteopath. The accuracy in treatment lies in diagnosing in which direction the ilium has moved to set it back in position & later training the muscles so that it doesn't go back adversely. Good luck!