No Nose Job
Let's say I know someone who wants to have a nose job because she feels she has too much of a "Jewish nose" and she feels self-conscious about it and she says it affects her confidence and she's not happy because of it. Would that be an acceptable reason to do it? And is there anything wrong with it from a Jewish point of view anyway?
The Torah prohibits mutilating the body in any way. Therefore a person is not allowed to cut, scratch or gash the body, whether directly himself, or by having another person do so. In times of old, people would do this as an expression of mourning, or for spiritual elevation, or to seal a pact, or for any other number of reasons. Despite the fact that doing so might be for some significant or meaningful reason, it's still forbidden because it damages the integrity of the body. All the more so it's prohibited as an act of self-affliction, even if done for temporary alleviation, as in the case of what's become unfortunately too common nowadays - "cutting".
However, for the purpose of adorning the body, it is permitted to cut or pierce. The reason for this is that the person's intention is not to destroy the body, but rather to beautify it. So earrings are permitted for this reason, and the Torah also mentions the use of nose rings and other piercings that were practiced even by our Patriarchs and Matriarchs. Although this expression of beautifying and adorning is subjective and a function of cultural norms, much of today's piercings which are done to be cool by being shocking and grotesque probably fit under the first category of forbidden mutilation. Tattoos would be another example of forbidden cutting or piercing, despite it being done to beautify or adorn the body (and a specific Torah prohibition against tattoos).
Similarly, not only is it permitted to cut the body in order to adorn it; it's also permitted to do so in order to remove harmful or even unattractive blemishes. So surgery to remove some harmful situation, or correct some harmful defect is certainly permitted. And even cosmetic surgery to remove or cover some conspicuous and embarrassing blemish like a mole, birthmark, scar etc. is also allowed. This is so even if the person's embarrassment seems exaggerated or unnecessary. Nevertheless, since he or she is sensitive enough about it to the point of wanting to remove it, they are permitted to do so.
The question is, “Where does removing a ‘Jewish nose’ fit into this discussion”? On the one hand, it clearly can't be considered mutilation since it’s being done to "enhance" one's appearance. On the other hand, it's clearly problematic to compare it to the removal of a mole or birthmark. If the surgery was needed to aid in breathing or to eliminate chronic congestion, for example, that would be corrective and permitted. And even if the person simply felt embarrassed by an oversized nose looking ugly or unattractive, that might also be acceptable.
However, it sounds like in the case of your friend, and that's certainly true in many cases, the only reason for having a nose job is to remove the "blemish" or "defect" of being and/or looking Jewish. This form of extreme, “neurotic assimilationism” is certainly unacceptable. The person would be better off learning to be proud of her Jewishness and working to acquire the level of maturity and inner peace to be happy with being and looking Jewish.