Sounds like a hip problem, Could be Wikipedia reference-linkSIJ or Lx Spine. When you see the doctor request a physio referral. It's been a month so the time for resting it is over you should get some physio intervention now.

You have no problem with externally rotating your hip but it isn't getting better... in this case I would suggest you try stressing internal rotation.
An exercise to try and see if it helps. Go into kneeling and put the unaffected side up. then bring the ankle of the sore side away from midline. Hand on back leg hip and other hand on chair for balance. Lean into the front leg but keep the body straight so you stretch the front of the sore hip with a bit of internal rotation.
Do that exercise with 2 seconds on and 2 seconds off and repeat 10 times... stand up go for quick 10m walk then try to do your rotation out to the right and see if it is better or worse... if better keep doing the exercise I'v described. Let me know how it goes.
If you don't get anywhere then best to visit physio as there are a few structures that could bring on your pain.