Your concern is shared by many people within the medical world as well as consumers and patients like yourself. As you have pointed out, the development of the X-ray machine followed by more advanced imaging tools such as CT scans, fluoroscopy, and MRIs has changed the way medicine is practiced. And with any diagnostic tool that can look inside the body, there are plusses (advantages) and minuses (disadvantages).
X-rays and CT scans do expose the body to ionizing radiation. That’s the type of radiation that has the ability to (potentially) disrupt cell structure and function, including disruption of your DNA. Unless there has been a traumatic injury or there is a strong suspicion of spinal fracture, infection, or tumors, imaging studies such as X-rays may not be needed. One reason to order imaging studies is when one of the treatments being considered is surgery.
With MRIs, there is no exposure to ionizing radiation. MRIs provide the only real way to look at the spinal cord. When you look at an MRI of the spine, you can easily see the bones, discs, spinal cord, ligaments, and even the cerebrospinal fluid in shades of black, white, and gray. Varying structures show up in different shades based on signal intensity picked up by the MRI.
MRIs are very helpful after trauma to the spine to look for neurologic damage. Likewise, vascular damage with blood loss or internal bleeding can be seen with MRIs. Pressure on the spinal cord or spinal nerve roots show up clearly. Injuries to the ligaments and other soft tissues can also be seen. Changes in size, shape, and orientation of the muscles are also visible. Any part of the spine from the head down to the tip of the spine (the coccyx) can be viewed.
There is one website we can direct you to for more information on radiologic testing including specific effects on the body and accumulation of radiation dosage: http://www.radiologyinfo.org. This website is provided by two groups: the Radiological Society of North America (RSNA) and the American College of Radiology (ACR). You will find a wealth of information there to further answer your question about measuring radiation dosage and safety.