Shaky hands is a common symptom that can occur in a variety of health conditions, and even in healthy individuals. The most frequent cause is a essential tremor, or familial. This is a benign inherited disorder. Is there anyone in your family with similar symptoms? Shaky hands can also be a sign of low blood sugar. Do you get this after not eating for 4-6 hours? Alcohol or caffeine withdrawals, and drugs for antianxiety, blood pressure withdrawal can frequently cause this as well. It can also be an indication of a more generalized medical condition such as neuromuscular disorder, and in diseases that affect the central nervous system (CNS). For example, brain tumor, Multiple sclerosis
or MS, Parkinson's disease, and overactive thyroid disease i.e. Grave's or hyperthyroidism can all present with shaky hands.
In all circumstances your emotion will tend to exaggerate this symptom so it makes sense that you would notice it often when you are fatigue, angry, scared or sad. Your young age put you at risk for "essential tremor" as mentioned above but you should definitely see a pediatrician
to rule out treatable conditions. He/she will want to know whether you are taking any medications, if you drink caffeinated beverages on a regular basis, if anyone in your family with similar symptoms. They may need to run a few blood tests and possible imaging as well.