my ring and pinky finger tremble?

This is not probably anything to worry about. I have noticed this at times myself. I would definitely not see a doctor about it. However, when you have your next regular check-up, mention it to the doctor. It is a good idea to have notes on what happens, what you notice might be causing it, etc., so you don't forget. In the course of a doctor visit, people forget.
And if you don't get regular check-ups, you should.

This obviously is bothersome to you, so develop strategies to keep your hands busy. There are different ways to conceal this, such as folding your hands together in front of you lightly when talking with someone. You can also get in the habit of carrying things in your hands, as this will help mask the tremors. Also simply putting your fingers very loosely in a fist (not really a clenched fist, just closing the fingers, and perhaps pressing the fingertips lightly against your palms. Experiment. Get creative. You should be able to find lots of different strategies that will work for you.

If you look at your fingers, they will tremble more, so get in the habit of ignoring it entirely.

If it gets worse, of course then it is time to have it looked at, but the chances are there's nothing you can do. A doctor might conceivably prescribe some medication, but for heaven's sake, avoid that at any cost. Meds to combat a tremor can have side effects.

You should mention this to your parents, and to your doctor the next time you see him. This could be a sign of a pinched nerve which could be important -- or not important at all.