I guess it is a case of its better to be safe than sorry, and get things checked out sooner rather than later...

That said, my sister has a constant slight tremor in one of her hands which is entirely normal for her - so it could just be something that is normal for you.

(I get tremors in both hands if I have low blood sugars, and really start to misjudge distances - was terrible when I used to work in a kitchen as I would get tiny slices on my index left finger - I would misjudge while cutting with my right hand...)