I used to manage a Group Home, and it would depend on your company policy as far as the drug testing. And again if they did request testing they won't be looking for Lithium. A lot of people take Ativan so those aren't the kinds of things they would be looking for.
If you are doing your job, it shouldn't be an issue. If you are worried about the shaking and someone notices you could just say you take medication and sometimes you shake. You don't have to tell them what it is, a lot of people take medications for blood pressure or whatever. You could even say your blood sugar is low and that's why you shake.
I think it is wonderful you are working in the group home and helping others, we are in a unique position to help others with disabilities as we understand.
Try not to worry about it so much, and enjoy your job a little!