I agree that your back pain can be due to gut. The large intestine (whole of the colon) lies on the inner portion of the back (retroperitoneum). The movement disorder of the large bowel can be responsible for your symptoms. You should get the following investigations which are the mainstay of the evaluation for your symptoms;
1) Blood investigations do give the clue. A complete blood count, biochemical profile, serum calcium, blood glucose, and thyroid function tests are routinely recommended in the evaluation of patients with these symptoms swollen abdomen (bloating / distension), intense lower back pain and constipation.
2) Depending on these blood results further blood work is done; serum protein electrophoresis, urine porphyrins, serum parathyroid hormone, and serum cortisol levels, may be done to identify or rule out myeloma, porphyria, hyperparathyroidism, and Addison's disease. These causes are not common causes so clinical manifestation and physical examination clues are important.
3) Barium enema or barium meal with follow through study
4) CT scan
6) Colonic transit time; it can provide a better understanding of the rate of stool movement through the colon.
7) Other investigations like Anorectal manometry, balloon expulsion test, Defecography etc.
8) Colonoscopy / sigmoidoscopy
9) Laparoscopy; camera exam of inside of the abdomen.
Your symptoms can be due to;
1) Intestinal motility disorder
2) Irritable bowel syndrome
3) Congenital band or internal hernia of the gut
Please feel free for your follow up questions.