It's possible you're anemic. Do you ever feel dizzy?
I've been anemic most of my life ( lack of iron) my hands would shake alot and I'd feel dizzy. You can get over the counter vitamins for it. It helped me a lot.
My left leg sometimes (only rarely) shakes for some reason.
Some blood tests I had for an unrelated issue showed I was borderline anemic. That might be something to look into.
you use your right hand too much..for whatever reason
Are you on any medication?
Zoloft used to give me tremors. Exactly like the way you described. It was frustrating.