I had a similar situation in my 1st trimester with shaking. Found out my blood pressure & blood sugar would drop at the same time. I would also get very dizzy & heart would race. Not sure if that matches anything you're feeling,but you might wanna get a blood pressure monitor at home & check yourself when you feel like that just to be on the safe side.
Nope. Dr didnt mention anything about shaky hands.
Yes, your heart is beating faster to accommodate extra blood volume. Why did dr say your hands were shaking?