You are not paranoid. Yorkies, especially very small ones like yours, are at greater risk for injury and illness than a lot of other dogs.
I was surprised by the difference between Max, my first Yorkie, and previous dogs my family had -- the work that is required to keep Max safe. The first year was the hardest for me in terms of worrying. Max will be 5 this month.
Don't let worrying get in the way of enjoying your pup.