I have personally been on lithium before as a long term mood stabiliser (not on that mood stabiliser now). It caused the same effect of hand tremors as you. And I can totally relate when you say you feel the antidepressants didn't give you much luck because boy have I had that in the past too.
I am sure that your doctors that have prescribed this for you have taken all factors into account and are hoping that this is something that will help you best in the long run moving forward. It's really hard when we're in that deep dark place and I'm sorry that you were in a crisis centre
I hope that you are able to find a sense of peace and comfort soon.