If the hand tremors persist, I should probably see a doctor, right?

I'm a bit worried because I've been experiencing persistent hand tremors lately.

Even when I just keep my hands still while getting my nails done, my fingertips tremble slightly. The shaking has also gotten worse when I hold my camera to take photos.

In the past, it used to be just a brief moment when I was nervous, but lately, I feel it even when I'm not particularly stressed.

I searched online and found mentions of caffeine and stress, as well as suggestions to get a neurological examination, which just makes me more confused....

For those of you who have been to a hospital for hand tremors,

could you tell me what kind of tests are performed at a neurology clinic?

If there are any places in the Gangnam area I can visit after work, please recommend them as well.