If you express your concerns to your doctor, he or she should be able to help you narrow down your choices. A history of what happened and what your symptoms are will guide the physician. A physical exam can also help identify the potential problem.
X-rays may be of limited value for soft tissue injuries. Bony fractures and bone spurs show up on X-rays. The doctor also looks at the joint spaces to determine if there's been a ligamentous tear. Whereas a narrowing of the space occurs with degeneration, a widening of the space is seen with ligament rupture.
MRIs show areas of thickening of the ligament from chronic injuries. If a contrast dye is used, then leakage of the dye into torn tissue can be seen.
Not all tears will show up on MRI so sometimes an ultrasound (US) is the best diagnostic imaging study. US shows joint spaces as well as an X-ray or MRI. Arthroscopic exam is not advised because too often the surgeon can't see a torn ligament if that's the problem.