Ahh, but here is the good news - you need not stop all resistance and strength training due to a shoulder injury! The PT can show you many safe exercises to do. Also, there are shoulder-sparing positions for doing planks. I cannot due a standard plank due to arthritis in hands, elbows and shoulders, but can do modified versions on my forearms. And resistance doesn't always mean machines at the gym. We use a variety of resistance bands and even our body weight to exercise because we travel, and finding a good gym isn't always possible.
Sue

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!

You may not have a rotator cuff tear but it may be inflammed. That was my issue. After an MRI showing that for my shoulder, the doctor put me through a range of motion exercises to see at what point I would feel pain. Based on that she recommended PT to help develop the muscles around the shoulder joint and over time the inflammation disappeared. All of out joints work well if the muscles supporting the joint are developed enough to support full range of motion. That means keeping up those exercises once you have healed as well to prevent injury again.