Hi, thanks for writing to HCM.
From the description of symptoms, I don't think your hip pain
is muscular in origin as the muscle pains seldom goes beyond 3 weeks.
Pain arising from the hip joint perse will be worsened by activity and gets relieved by rest.
Posterior pain and buttock pain is most often associated with Lumbar spine
So I suggest you to consult an orthopedic surgeon for a detailed evaluation and management.
Hope this information is helpful. Good day