I've used tooth paste on my headlights before and it doesn't work.
The plastic used on modern headlights is Polycarbonate. So all you gotta do is sand the headlight with a real hi-grit sandpaper (like 2000-2500) and spray it with a UV resistant acrylic sealer.
If you want your headlights looking brand new, open the lights up and sand on both sides then coat it with the sealer. You can fix even the most fucked of headlights like that.