If there's a burning pain, a tendon or ligament in your hip is probably inflamed due to aggravation. I think it could very well be bursitis. Bursitis pain can come and go like you described, which is why some days you can walk and some days you can't. It also can be very painful at night when lying down.
I had hip pain for years and finally went to an orthopedic surgeon after being put through PT, which did nothing for me. I was given an MRI, it came back healthy...an injury won't always show up however on an MRI. I was given a cortisone shot which helped a lot. I now do exercises to strengthen the area, my hip has been so much better.
Don't turn down a cortisone shot, the hip area responds well to these. I'd also take the muscle relaxer, it'll help you sleep and could even relax the muscles well enough to allow some healing to happen.