Hi Lisa,
It's great to see you stopping by!
Your doctor probably thought you might be hyperthyroid (overactive gland) or heading that way because hand tremors are a common sign of that. Also with an overactive thyroid you would usually lose weight rather than gaining however, with a common autoimmune thyroid disease called "Hashimoto's thyroiditis", you can be heading toward progessive hypothyroidism (underactive) but have periods of hyperthyroid symptoms along the way.
If by chance your doc could give you that thyroid test result, you might check to see if it was a "TSH only" test or if it also included the T4 level which would be more thorough and if tests for "thyroid antibodies" were included. I mention this because autoimmune thyroid disease can cause symptoms before thyroid hormone imbalance occurs.
By no means does it mean a doctor isn't great because they don't do more thorough thyroid labs but some don't specialize in thyroid, so don't really know to add these tests.
Hand tremors alone can mean other things of course but I've always been of the opinion, since researching thyroid, that to rule thyroid problems out, it's better to have all the related blood tests.
If you have any other symptoms like increased fatigue, thinning of eyebrows, hair falling out, changes in your skin texture (more dry or oily), changes in bowel function, changes in sex hormone related functions, etc..., ruling out thyroid disease becomes even more important.
I gained lots of weight just before diagnosed with Hashimoto's caused hypothyroidism and I have a great more difficulty losing since having the disease, even though I'm well treated for it. It takes me more effort to accomplish weight loss/control.