The purple patch is probably a hematoma or localized collection of blood. It could also be a bruise.
Yes, it is best to go to a hospital. You may need a fresh set of X-rays. You may also need MRI. Yes, you may need a cast or a sling depending on type of injury and you need to rest the shoulder. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.