Burning pain sounds neuropathic to me. Generally follows a "Glove and stocking" peripheral neuropathy pattern but can sometimes just pick out one nerve root. So I have seen burning pain in a band on peoples' trunks and once it occurred when someone passed urine (urinary tract infection excluded) - so rare. And generally no way to proove neuropathic in origin. But the root distribution pain often seemed to occur after a short period of high glucose levels and would often settle after 4-6 weeks improved control.
Apart from high glucose levels, I am not aware of any other risk factors that one should look at, but I'd optomise vitamin D levels anyway and might as well heck B12 level and thryoid function.
In terms of treatment, good glucose control seems important; I guess that one could try the drugs / tablets that one uses for standard neuropathic pain such as pregabalin, gabapentin, duloxetine, amitriptylline etc, but would avoid the topical things like lidocaine or capsaicin given the location of the problem. But if you do try something, it would be worth reviewing the prescription after 6 weeks of improved diabetic control cos problem might have resolved by then
So I don't think that it is related to the sitagliptin
best wishes