I am sorry that you feel so poorly, but welcome to the board.
If you think it could be a celiac, you should request celiac disease blood tests and possibly an endoscopic biopsy. The bloo tests are:
TTG IgA and TTG IgG
total serum IgA
DGP IgA and DGP IgG
AGA IgA and AGA IgG (these are older and less reliable tests)
You must be eating gluten in the weeks prior to your test so do not start eating gluten free until you are done testing.
If your ceiac tests come back negative, and you suspect gluten is the cause, there is a chance that you have Non-Celiac Gluten Intolerance (NCGI) which has all the bad symptoms and inflammation as celiac disease but does not involve damage to the small intestine (villi blunting). There are currently no medically recognized tests for NCGI, so you would have to commit to the gluten-free diet for a few months and wait to see if your body feels better without gluten.
I do not often hear about pain that radiates to the back that is caused by celiac disease. My first guess would have been a kidney, pancreas, or a lymph problem. It is good you have had those checked.
I hope you feel better soon.
Thanks for prompt response.