Chad Waterbury and others suggest we avoid straight bars for these exercises.
Option A would be rings or 2 handles that move freely or option B neutral grip.
If we look at martial arts each punch we do involves some rotation so i allmost never use any straight bar/handle.
For vertical pulls i use dumbells, also for shoulder press, for pulldown i use 2 handles, etc...
My shoulder problem is over for 12 months so i read about that subject and it seems our body structure is often a bit off and many exercises create problems when done the proper way according to most books/articles.
After some rest and maybe some rehab you should be fine staying away from bad options for you.
On youtube you might find videos if needed for rehab.
All the best !