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May I ask, how old are you? Did your father or grandmother have any diagnosis other than "familial tremor" or "benigh essential tremor"?
The most likely diagnosis is familial tremor, or benign essential tremor (same thing). This is a diagnosis of exclusion, meaning that other causes must be ruled out prior to arriving at it. However, it is not difficult to rule out other siagnoses, such as Parkinsons Disease, stroke, and others. A very good patient education page on this can be found at: http://familydoctor.org/online/famdocen/home/common/brain/disorders/807.html.
I hope this helps.