There is no relation between shoulder pain and ovarian cyst. Chances are you strained a muscle in your shoulder but there is no way the two could be related to each other.
Generally no, shoulder pain would not be related to an ovarian cyst. Your ovaries are located much lower down, near your hips - so cysts may cause you to experience pain near there.
Yes. If you have an ovarian cyst that has burst, or have recently had surgery for cysts, the pain could be related. Call a doctor right away as this could be a sign of serious side effects.