X-rays have limited value in a case like this. Your doctor might have ordered an X-ray if she thought you could have fractured a bone.
MRI (magnetic resonance imaging) is a useful test to identify damaged shoulder tendons. However, it is not always necessary to perform these studies. MRIs are very expensive, and most tendon tears can be accurately identified with a careful physical examination and history.
An MRI is probably not necessary unless the doctor is considering surgery. If you do not get better after a program of physical therapy, the doctor may reconsider ordering an MRI. Getting a second opinion from another doctor may confirm the diagnosis at a lesser cost.