When someone requests that you use 'rouge' (not as in the color of something), what do they mean? Do they mean lipstick or blush?

It can be used for both if used sparingly.

In the United States it is blush, but, I think in some countries they refer to lipstick as "lip rouge." So, it depends on what country the person who said it to you is from. The best thing to do would be to ask which they meant.

It means blush.