It feels like it's my rotator or rear delt or something. Pain within the shoulder while doing pullovers may indicate a weak or damaged rotation cuff. You need to determine the extent of the limitation if you want to enjoy the benefits of the exercise.
Pullovers are, amongst other things, a great lat builder and a fun superset transition.
Some folks cannot do the movement due to sharp pain and uncontrollable shoulder dislocation. This is too bad, yet good to know for future reference. The limitations should be noted and the exercise put aside temporarily or altogether. The indication here is that the shoulder mechanics are abnormal or damaged and need special care. Any orthopedic can argue against the pullover as a favorable movement, the rotation cuff becoming the fulcrum bearing the greatest resistance during execution.