There's nothing obviously wrong here. It was a strong, controlled bench press. The bar does shift back a little first thing off the chest, which may be causing your elbows to flare slightly and bother your shoulders. It also looks like your grip may be wide. Those are two things to work with given that your shoulder is pissed. Narrow your grip and keep your elbows tucked a little longer during the first part of the push. Does the bar you are using have dual score marks? If so, move your grip in so that your pinky is grazing the inside score mark and see how that feels. You might need to take a few pounds off the bench to get comfortable with that at first.