Not sure how old you are, but my wife is in her early 50's and has been suffering from a hip labral tear
brought on by too much yoga. Her symptoms seem similar to yours.
...Athletes who participate in such sports as ice hockey, soccer, football, golfing and ballet are at higher risk of developing a hip labral tear...
Interesting that hockey, ballet and golf are similarly hazardous. :-)
There are a few injections she's tried, and a surgical procedure that has attempted to anchor the torn labrum, but so far nothing has been curative. Hope you're not similarly afflicted.
Might be worth looking into the illiopsoas, too...I have some abdominal scarring that has led to issues that range from where the rectus femoris inserts into the pelvis, up through lower abs into the psoas insertion point, and then along the psoas to my lower back. Stretching groin muscles and the rectus femoris (couch stretch) helps immensely, as does soft tissue work on psoas, lower abs, and rectus femoris insertion point. Tight left rectus femoris usually shows up with right psoas issues. Running and cycling make it worse - cycling especially because a tight psoas gives you a functional leg length difference.
Awhile back, the running specialists at the Pentagon (yes, that's where they hide them...with all the 40-50 somethings who mostly can't run anymore...???) filmed me running and caught me dropping a hip on my weak side. Then they put me through a core work-up and gave me several sets of very targeted exercises. At first, it made things much worse, but then it got a lot better. Now I only have problems when I do situps, and since I just took my last APFT, I'm done with those. But I relate all of this because core/abs/hip issues seem to be rather complex and interrelated - you may find challenges and solutions in unexpected places. Certainly lots to read on the internet. So now you have another search term - may one of them bring you some ideas for resolution.
My wholly inexpert opinion is that the hip labrum is not the culprit here.
I have already given the illiopsoas some consideration, enough to even attempt to learn how to spell the thing rather than just use cut and paste techniques.
This is a very busy part of the body, enough so that I may have to refine my approach to a differential diagnosis (is there where I have to admit I have been using "eeny, meeny, miny, moe"? who's moe?).
Probably it was a mistake to omit any stretching/strengthening exercises for the past 6+ weeks, and all I can say is it wasn't foremost in my mind. But, I'm back at it now, and I remain somewhere between hopeful and confident that eventually I will hit upon something that will lead to improvement. And, if not, then I can always simply abandon running and turn to some new promising arena, say, body building or, perhaps, becoming a missionary of sorts and going around talking people out of their errant ideologies.
Birdwatching. It's all the rage these days.