While bench pressing isn’t inherently bad for your shoulders, poor technique and excessive loading and training volume (like anything) can cause great shoulder problems and pain. If you are experiencing pain during the bench press, stop doing this movement and allow for the joint and connective tissues to heal and rest.
After addressing your limitations with a medical professional, you could integrate pressing movements like the floor press or swiss bar bench press, as well as work on proper setup and scapular stability in the bench press.