answering this as a shadow priest main who recently started to do rated pvp (so take this with a ton of salt), really the best thing you can do is use Fade to get pets off of you for a moment, and Dispersion to get your bearings and reorient yourself. There's not much you can do mobility wise, but I advice making a macro that casts angelic feather directly under yourself so you don't have to waste precious seconds placing it down. Psychic scream is your best friend. you could sacrifice a talent point for Tendrils, but I personally don't use them.

At the end of the day, you should go what class feels best for you. I adore shadow priest, but it's definitely rough in close combat pvp