Phantom Limb. It is quite common for amputees to experience sensations on the removed limb. Many times it is pains, for others, it can feel different (itching for example). A study reported in nejm found that using a mirror to 'visualize' the removed body part actually helped resolve those sensations. http://www.nejm.org/doi/full/10.1056/nejmc071927. No matter what, discuss things with your doctor or surgeon.
See below. There are no blood tests or xrays mris etc that need to be done. The diagnosis is established by the person's history and physical examination. The treatment includes various desensitization techniques such as tapping the limb, massage, using a prosthesis as well as various medications designed to dampen overactive nerves.