Put on a pair of glasses then go back to the mirror and take them off. If you do something temporary like this then the mirror should update your face. If this doesn't work then you could try using the facelift machine (which also updates your face, but you need to change the face a little for this to work), which I think is the showbiz career reward. Get that by entering "boolprop testingcheatsenabled true" in the cheat prompt then shiftclicking the newspaper and selecting 'career rewards' then 'showbiz'. It won't spawn if your sim is doing anything, so you should temporarly turn off free-will which is under game options.