Hi. Thanks for your query. Noted the history and understood the concerns. Very foul smelling diarrhea with lower back is most probably indicative of an intestinal infection needing an active clinical evaluation, examination and proper management. One week is a long time to suffer, hence I would advise you to send your Stool sample for full tests. Blood for diabetes , CBC, and liver function tests. Ultrasonography of the whole abdomen. Get started on a proper antibiotic, metronidazole, probiotics and symptomatic management. Take plenty of oral fluids. Boiled and cooled water. Eat only home-made fresh foods. Take a review till fully cured. I the problem persists even after such a treatment then you may need a second opinion of a Gastroenterologist and colonoscopy for further evaluation.