I just had a rotator cuff strain injury from a fall. Can't lift my arm up. How long does it usually take to recover? When can I resume playing sports

Best for you to get. Advise from someone who evaluates you, by examining/investigating you. He'll inform you of the diagnosis/treatment. So see an orthopod. It generally last for about 6 weeks, by then if its a partial tear/sprain, it should improve greatly. A few patients don't improve and may need MRI and probably benefit from the surgical repair. Returning to sports would be once the rc has healed. Good luck.