Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is nor can I recommend specific therapies for you. However I will try to provide you with some useful information.
Given your symptom description, the diagnosis that comes to mind is called Essential tremor. This is a high-frequency (rapid) tremor that most commonly occurs in the fingers/hands but can involve the head, voice, and sometimes the legs. It is present with activity and worsens with stress and anxiety. It can start at an early age or in late adulthood. The diagnosis is made based on clinical findings, there is not test for this condition.
Essential tremor is hereditary (it runs in families), and the fact that your dad had a tremor too supports this diagnosis. One feature of essential tremor is that it improves with alcohol intake. The good news about it is that besides the tremor, which is of course very bothersome to some people, it does not have other consequences (it is not neurodegenerative), though about 20% may develop Parkinson's disease later on in life. There are several medications used to treat essential tremor, including propranolol, topamax (which it sounds like you are on for headache so that might be useful for the tremor too at the right dose), mysoline, and others. If the tremor becomes debilitating and starts affecting daily life and occupation (which happens in some people but not others), there are surgical options available (called deep brain stimulation, which at this time is only done in a few centers in the world but seems highly effective).
It is a good idea to see a neurologist because he/she can assess you and consider all possible diagnoses, and if essential tremor is diagnosed, provide you appropriate therapy.
Thank you for using the forum, I hope you find this information useful, good luck.