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I'm no expert but I've certainly heard of people recovering from surgery after labral tears. As a related comparison, I've had keyhole hip surgery for femeroacetabular impingement (FAI) and whilst having as much time out from running as I did was extremely frustrating (on the bright side I got right back into cycling in a big way!) the surgery was 100% successful and I've hit big PBs across all distances since the surgery, with four years now relatively injury free. Best of luck getting treatment and I hope you can return to running long term.
Turns out that my hip pain is not muscular or ligament related, but labral tears.
Probably in both hips.
So no more running then.
Bugger.