Symbolic dice, or a better option?

Generally what I want to do is roll 3d6 and put a result indicator in the toolbar. Like this:

Thus far the only way I think of how to do this is to use a symbolic die roll. With the symbolic die I need to create a face for each chance of a given number. That means 1 face for a 3, 3 faces for a 4, 6 faces for a 5, … 27 faces for a 10, ect.

So, firstly: Is a symbolic die really my only option?
Second: If that is true, is there a way to weight the faces for higher probability?

Thanks in advance. (Probably later too.)