AlpakaDream: I'm not 100% sure but i think you can do that later when you have your own house.
I read in the manual that you can change your hairstyle/color/fashion there... Oh I will see if it includes face lifting. Thanks for now; will mark it as solution if that did the trick :)
edit:
Nope, just got my first home. Only the above mentioned; face type cant be changed there. Weirdly; in the customization I again thought "Oh, ain't that bad after all" till I exited. Lighting? Angle? IDK *sigh* :/
Guess I have to hope that something resembling a mod community gets interested in the game.