I totally get that you care more about strangers' opinions rather than people close to you. My problem is that I don't really take compliments very well, no matter who they are, unless I am satisfied with something completely — and by satisfied I mean it would stack up next to the best in the world, which obviously they never will. So I am chronically dissatisfied :) Just have to let it go and not worry about it too much.
But it's better to be good but think you're bad than be bad and think you're good! So it's good to be a bit self-critical but also to listen to those around you. Experience will also boost confidence.