Big pains generally do not go away after 20 minutes.
Your squat doesn't look great, but it doesn't look particularly injurious, either. You lift your chest quite a bit during the middle of the ascent. This may cause you to overextend your back. Cannot really say from here. I can tell you that you need to contract all of your muscles harder and get tighter. Stay with your hips. Drive your butt up the whole way to the top. Don't try and bend the bar across your back. That can bother shoulders and elbows.