Burning pain in hips and lower back pain seem to be due to neurological causes or spinal cord causes. Burning pain and sensation is often symptomatic of nerve related causes. I suggest you to get a MRI scan of the loser spine done to confirm the diagnosis.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.