Lasso select + edit->convert to drawing colour?
Or make a layer above the one you want to modifiy, clip to layer below and paint where you want the white to go?

That'll put the white in the places you want while keeping to whatever is on the layer you're editing, unless you were looking for something more complex than that?

Sounds like a combination of things:

1- The tool "Figure" I believe has a Lasso fill sub-tool, it'll fill in with the primary chosen typically. Think it's in the tool with radial burst and speedlines if I recall correctly. In "Direct draw" with the lines and circle shapes.
2- In the "Layer" dropdown, in "Layer Setting" you can click "Lock Transperent Pixels" -alternatively, on the Layers window to the right of the "Lock layer" symbol is also a "Lock Transparent Pixels"

Hope that helps.