I'm not going to lie to you. This is going to suck.
I experienced the exact same thing you are described. It developed gradually while doing Smolov, and I had to quit the cycle because of it. I did a ton of research and saw numerous physios/sports med docs, and none could give me a definite answer in terms of what it was. It was most likely hip tendonitis, according to the last sports med doc. Regardless, it got better by taking several months off squatting, and PVC rolling my hips every day. Try to get the roller right in the area that hurts when you squat. For me, this was right in the hip crease. Probably shouldn't static stretch your hips, as this can irritate it further until your hips are healthy. As a result of the experience, I have to be much more dilligent about warming up my hips/lower body. But I'm able to squat again, and am slowly getting back to where I was before. But since it took 5 months for the pain to go away, I lost significant squat numbers.