Hello, and thanks for writing in.
With limping in general, there are a few main categories of problems causing it: a fractured bone, dislocated joint, or a soft tissue injury (strain, sprain, etc.) There are a few other possible causes, such as a bite wound after an injury, pinched nerve or herniated disc in the neck or back.
To answer your question...YES, I would highly recommend getting X-rays taken to get more information about the bones and joints, since there are some abnormalities that can't be felt on exam. So, the X-rays will certainly help. Then, more specific treatment can be started, depending on what is found.
I hope this helps.