When I don't drink my arms begin to shake, is this normal?

Alcohol? Do you mean alcohol? If you consume more than a couple of drinks daily, you may have alcohol dependence. Stopping leads to withdrawl symptoms, including shaking or seizure. The most severe form is delirium tremens, with loss of control of blood pressure. If this the case, please seek help from a physician for treatment options. Liver damage, nerve disorders and electrolyte problems can also cause.
No. If you are referring to alcohol, tremors that occur while abstaining from drinking may indicate a dependence issue. You should discuss this in more detail with your family physician. If you are referring to water or other beverages, tremors or dizziness may indicate dehydration. A good rule of thumb is to drink small amounts often throughout the day.