There are many possible sources of shoulder pain. The rotator cuff (RTC) may be one of them. Damage to the RTC ranges anywhere from an acute strain to a full tear with many variations in between.
MRI assesses the integrity of the rotator cuff tendons (there are four tendons total). Signal intensity helps show areas of irregularity and thinning. Usually a patient history (how the injury happened, what makes it better or worse) and physical exam are also needed to make the final diagnosis.
Whether or not to have an MRI is your decision. Your physician can help you by offering pros and cons based on his or her findings after the history and exam. The cost of the procedure may be one consideration.
But keep in mind that the MRI helps pinpoint the exact problem. This makes it possible to plan the most appropriate treatment known to work for that problem. You save time and money this way and optimally gain pain relief and improved function faster. This allows you to get back to your normal daily activities, including work.