There are various causes of a burning sensation in the
lower back, which could range from muscle sprains, or spasms, infections like
herpes zoster and conditions like pinched nerves. Zoster symptoms would be dermatomal in pattern and there would be skin lesions like blisters, limited to the area supplied by the affected nerve. Since you have the burning sensation extending to the hips and down until the feet, I suggest that you consult a neurologist soon.