Do you play any sports? Or have a job that requires you to sit a lot or other possible weird things?
Usually some ball sports where you're throwing can jack up mobility issues in your hips. Same with too much sitting.
How tight are your left hip flexors?
Put heat on your hip area around the greater trochanter, hip flexors, and adductors too for about 10-15 minutes. Then loosen them up with massage for 10-15 minutes. Then stretch them out with some PNF for 10-15 minutes.
Get the adductors, hip flexors, external and internal rotators, and IT band. See how it does if you gain more mobility.
Here's internal rotators stretch:
Rest you can look up on youtube if you need help.
I am almost certain it's likely your left hip flexors and adductors giving you issues. If they're too tight then when you try to rotate your hip you can get some impingement of the joint which is what you're feeling "pinching" as you rotate.