The Ready State Virtual Mobility Coach is like having a virtual Kelly Starrett in your pocket.
Have you looked at your technique for pull ups or dips?
Some may come from the position your shoulder is in/technique for each skill.
Carl Paoli has some great progressions and transfer to clean up pull up mechanics
Blocking Movement for Quality Pull Ups
It could be your grip on the bar. Start of a 7 part series:
Pull and Grip Strength Progression Pt.1