I've got a bit of a tremor as well, similar to yours. When I first started operating as an ophtho resident, it did not help things. While I could still operate, unfortunately, if things are going badly in the case your tremor just gets worse. Also, sleep deprivation makes it worse, so post-call days were difficult. I imagine it also makes the attendings supervising you a bit nervous because the tremor can be prominent under an operating microscope.
So the things I learned to do that helped: I cut out caffeine completely. I stopped any weight lifting or exercise the day before surgery. Tried very hard to schedule cases on days when I would not be post-call. As, Slide said, you learn to support your hands while operating. And finally I started taking a low-dose beta-blocker prior to surgery. (a little wine makes essential tremor improve as well but there are some ethical issues with drinking prior to operating.. 😉)
After all that, by the end of residency several of the attendings mentioned that I was one of the best residents they had trained surgically. It's still a bit of a pain in the butt to do all of that though, and when I started operating I had doubted my decision to do ophtho. This would not be an issue in most surgical fields (can you imagine an orthopod not weight lifting the day before surgery?).
So if you really want to do ophtho, I wouldn't let this stop you. But if another medical field makes you equally happy, I might consider it.
One other thing, get your disability insurance before you let anyone diagnose you with essential tremor (or any other kind of tremor).
