I've had pain when taking a deep breath in my back and chest i have a rotator cuff injury that is said to have caused this but i think it's a pe?

Causes of PE: PE and DVT are caused by either prolonged periods of not moving, injuries, or genetic clotting disorders. In the absence of any of these, why would you have a PE. also, typically there would be a leg clot. Is your leg swollen? I agree the RTC tears don't typically cause back or chest pain but there are many other possible diagnoses, such as costochondritis, that would be more likely.