I suspect it's a tendonitis issue if the pain goes away the more you squat.
I've battled with this problem.
A few things that seem to have helped:
- taking a magnesium supplement. It relaxes the muscles and supposedly helps remove the calcification in the tendon scar tissue. I'm taking twice the recommended dosage (you'll know you're taking too much if you start getting "loose stools").
- foam rolling/massaging with some kind of cylindrical object. Breaks up the scar tissue and helps the damaged tendon fibres to heal in better alignment. I also froze some water in a cylindrical drink bottle and rolled on it. The ice gets more blood flowing into the damaged area.
- defranco agile 8 routine before workouts.
- I stopped trying to shove my knees out in the bottom of the squat. After reviewing my videos I realised that my knees were actually going out wider than my feet. I don't think that's an issue for you though, judging from your videos.
Hope some of that helps.