Binding will definitely damage breast tissue even when it's fully developed, and is NOT a good idea while developing.
However, I had good luck (up to a point) with wearing a compression sports bra - *not* one too tight or that was smaller than my size, just one listed as "high compression" or "maximum bounce control" - under a T-shirt, with a loose shirt over that. Basically, the goal was to hide that telltale silhouette by making it look like I was just chubby or in baggy clothes.