I would recommend that you see a primary care doctor
for your symptoms. While you may need a specialist, a primary care doctor can often diagnose and treat your symptoms. Especially in your case, it is not clear what the cause is, so the primary doctor can also refer you to the appropriate specialist.
To begin, it is not clear that this is hip pain. Despite common perception, the hip joint is actually very centrally located, so hip pain manifests as pain in the groin or sometimes in the buttocks. Pain on the side of the body is rarely caused by the hip joint.
The symptoms of pain going down the leg could be consistent with sciatica. Sciatica is a condition where the nerve is compressed coming out of the spine, therefore causing pain over the distribution of the nerve. This compression can occur because of a broken bone or simply from wear and tear on the spine with age. This is known as degenerative joint disease.
There are other causes of pain. Trochanteric bursitis is a common cause of pain on the side, but rarely goes down. Iliotibial band syndrome can cause it as well.
Talk to a primary care doctor. He or she can help manage many of the above conditions.