obviously the most important thing is to mind that injury.
Pull ups if you want good results you will want to do them 3x a week but again take it easy. I would suggest Australian pull ups as a supplementary pulling exercise since it is easier than pull ups and may not aggravate your injury as much, yet it is also a great exercise in its own right.
Deadlift and military press are great lifts! If your goal is overall injury prevention, generally I would suggest focusing more on bridges sooner than adding deadlifts, but again whatever doesn’t aggravate your injury.