I personally would start with a fellowship-trained orthopedic spinal specialist. Your hip pain very well may be a referred pain caused by a lower back issue, or even an SI issue. The orthopedic spinal specialist could tell a lot from examining you and looking at imaging studies that he would order. If it turns out to be a hip problem, s/he will refer you to an ortho who specializes in joint problems.
I was diagnosed with SI problems and facet arthritis by my Physiatrist who is a Spine Specialist (a Physical Medicine Doctor). He has been extremely helpful in treating my lower back and sacroiliac. Take care, Kera4