1. is grammatically correct, but would never be used.
2 and 3 are incorrect.
Usually when something fills you with fatigue, you would usually use it as a passive verb.
I am fatigued listening to so much classical music.
Classical music just fatigues me.
The term 'beauty fatigue' refers more to the feeling of fatigue that woman get trying to live up to the high standards of beauty set by women's fashion magazines.
Note to women: Beauty magazines have only one purpose that I've ever been able to find - to make women feel ugly and thus sell more 'beauty' products. If you listen to their advice, you will be extremely unhappy. You will also probably develop some eating disorder.
[Sorry for the rant. I will now get down off my soapbox]