A tremor in your hand or other body part should be evaluated by a doctor
sooner than later. This is because there are many different conditions that can cause a tremor and they often have different treatments. The most common cause of tremor is a condition called benign essential tremor. This is a condition that usually runs in families where a slight tremor occurs usually in the hand. It is worsened with stress of stimulants such as caffeine and it gets better with relaxation and consumption of small amounts of alcohol. This type of tremor is only treated if it is really bothersome, but a low dose of a medication called propranolol works quite well. Other causes of tremor include diseases of the cerebellum (the back part of the brain) and Parkinson's disease. These are less common, but should be ruled out first.
I think you should probably schedule an appointment with a neurologist
. This is the type of doctor that usually sees referrals for a diagnosis of tremor. He or she will listen to your description of your symptoms and perform a comprehensive neurological exam. A diagnosis should be obtainable on your first visit allowing you to start treatment (if necessary) right away. Good luck.