NEVER, NEVER, NEVER put a larger fuse in than what it calls for. I am guessing that you have never had to deal with a car fire before? That is a sure fire way to melt wires which in turn lead to fires.
Why did you assume the correct wire is the red one? Did you test power to the wire? To be honest, no everything isn't working fine or the fuse wouldn't be blowing. It is blowing because it is telling you there is something shorting out or there is too much draw on the wire.
Why are you tapping fog lights into a wire that is only meant to handle low wattage parking lights? That might be your problem. Google the right way to wire fog lights and go from there. BTW, the fogs should be on their own fuse just as your head lights are on their own fuse as well as the tail lights and the parking lights. Fog lights should also be on a relay. Do you have a relay wired in?