Is there a left and right ballet shoe?

Yes and no. When you buy them, there is no definite left or right shoe whether it's a soft shoe or pointe shoe and even some jazz shoes. More in pointe shoes, as you start to wear them you decide which shoe works or feels better on which foot. The only time when you buy them, that I can think of, that you might have a right or left shoe is if one foot is bigger than the other. A lot of people (depending to the size difference) get two different pairs and each pair is a different size.