Hi @thisnthat, Hopefully, it's not a rotator cuff tear because they are terrible. I can't raise my right arm much past shoulder level. By the way, you can take tylenol to block pain signals with ibuprophen which reduces inflammation. I vary the two, depending upon what kind of pain I have. Were you told to ice it or do heat treatments?
You can still work the shoulder that isn't injured and that is supposed to benefit the injured shoulder. Just go easy, as it would be a real pain to injure both.
As @sueinmn mentions, there are alternate forms of planks and pushups, done from the forearms or even standing. Maybe PT would clear you for those. Good luck!