Kenneth from Canada,
Your grip looks fine from here, but I do notice that your elbows twitch a lot on the way up. Are you pushing down on the bar on the ascent as if you were trying to bend the bar around your back? If so, that could be the cause of the problem. Try and take your hands out of the equation. Given the extent of the problem, methinks a change is in order. If you are in acute pain outside of the gym and it is bothersome, take a loading dose of ibuprofen. 4 x 200 mg tablets three times a day for three or four days. Take it with food. That will knock down the inflammation and give you some relief. Next, switch to high bar squats for a time. There are people for whom low bar squats kick the hell out of their elbows, even without an obvious reason. Let's get this calmed down first and then rethink our options. I love low bar squats and they are what I teach to everyone. However, you can live a full and complete life squatting high bar, too.
As for your squat form, things are not too bad, but your knees need to be out more and you need to go deeper on a few reps.