You probably have what's known as "benign familial tremor", which is also called "essential tremor". Knowing the name of the disorder will help you to search for more information about it.
My husband has it, and like yours, it disappears if he has as little as one alcoholic drink. This is the hallmark characteristic of the disorder. It is not associated with alcohol abuse, but it does run in families. His father had it, as does our daughter to a milder degree.