Hi there. I'm the mom of a teen too and it is always worrisome when they have something like this. Believe it or not, tremors in teens is not uncommon.
There is a long list of what may cause it. Some I'd wonder about with my own teen boy are dehydration, stress/anxiety, low blood sugar, overuse or muscle injury (what is his job, does he use that hand/arm often?), too much caffeine. There are other potential causes as well.
It is good to see the doctor and I hope you report back what you hear! Since it is one hand, that leads to you probably worrying about Parkinson's but he is so young and onset would be rare for that. So, don't worry until you have to. Again, please let me know what the doctor says. My son has a lot of anxiety and high school is rough. He can have slight tremors and it is stress related.
Great, please do update us. It kind of makes sense that he is doing a lot o burger flipping and having issues in one arm. My guess that is related to what he is dealing with. It would be nice to have an explanation like that, right? Kids sure do worry us!! So, please do let me know what the doctor says!