Sounds like a mobility issue I had early last year. You probably have tight hip flexors, and since it's bilateral, your attempts to squat deep are probably aggravating them. You need to rest from squatting for a few sessions and try really stretching them out for 2 mins per side 2-3x a day. Also do deep squat sits and use your arms to push your knees out and hold for a couple of minutes 2-3x. Get a hard ball like a cricket ball or lacrosse ball, a foam roller doesn't really target the hips that well. Really dig into the tight areas with it for a few minutes each side. You can ice if you want but only for a couple of days if it's really painful, the true remedy is long-term stretching/deep tissue work.
