Rabbi Jacobovitz on Plastic Surgery
The problem was considered under four headings: the theological implications of "improving" God's work or "flying in the face of Providence"; the possible risks to life involved in any operation; the Jewish objection to any mutilation of the body; and the ethical censure of human vanity, especially among males.
In the sparse rabbinic writings on the subject, these reservations could be discounted, provided the danger is minimal; and especially 1) if the operation is medically indicated, e.g. following an accident, or for grave psychological reasons; 2) if the correction of the deformity is designed to facilitate or maintain a happy marriage; or 3) if it will enable a person to play a constructive role in Society and to earn a decent livelihood. ⁷

The second proof is fundamental to our discussion of plastic surgery, particularly cosmetic surgery. The Talmud [Shabbat 50b]¹⁶ states that a man may remove scabs from his body to alleviate pain, but not to improve his appearance. ¹⁷ At first glance, this may appear to exclude the possibility of plastic surgery. However, Tosofos, ¹⁸ commenting on this statement, promulgates a concept that demonstrates a very sensitive understanding of human nature and psychology. He writes: "If the only pain that he suffers is that he is embarrassed to walk among people then it is permissible, because there is no greater pain than this." Tosofos recognizes that there is no greater suffering than psychological pain and that it is very difficult to judge for someone else the degree of suffering they are experiencing as a result of a self-perceived defect.
(Daniel Eisenberg MD)

The Mishna [Ketubot 72b]²² discusses the case of a man who betroths a woman on the condition that she has no defect (mum) where a "mum" is defined as any defect that would bar a Cohen (Jewish priest) from serving in the Temple. Tosafos²³ states that if the woman had her blemish corrected by a physician before her engagement, the marriage is valid. Since many of the blemishes that would apply to a Cohen include cosmetic imperfections²⁴ of the face for which people today would desire elective plastic surgery and Tosafos permits these blemishes to be corrected by a physician, Rabbi Klein states that it appears that a man or woman may go to a doctor to correct a cosmetic defect merely for enhancement of their appearance. Rabbi Klein rejects the argument that plastic surgery entails any danger whatsoever based the information which he received from physicians.
(Ibid)

Chaim Jachter summarizing the Tzitz Eliezer
The Gemara (Bava Kama 85a) infers from the obligation that the Torah (Shemot 21:1) imposes upon an injurer to pay his victim’s medical bills that “The Torah permits a physician to heal.” Absent such permission, explain Tosafot (Bava Kamma 85a s.v. Shenitnah), we would have thought that we are forbidden to heal because we “appear to be contradicting the King’s decree.” By authorizing medical attention, however, the Torah teaches that we are not contradicting Hashem’s will, because the King who issued the decree for the illness or injury also permitted physicians to heal.
Rav Waldenberg forcefully argues that the divine license to heal applies only to curing an illness, not to altering one’s appearance. It is certainly forbidden, he adds, to risk one’s life to undergo cosmetic surgery, even if the risk is not great.
Rav Waldenberg even calls cosmetic surgery an insult to our Creator, because it implies that His work is inadequate. To prove this point, he cites a story in the Gemara (Ta’anit 20b) in which Rabi Elazar ben Shimon met an exceptionally homely individual and asked him whether all of the people in his town were as ugly as he. The man responded that Rabi Elazar had insulted Hashem by implying, “What an ugly vessel You have made!” Rabi Elazar sought his forgiveness, and though the man refused to extend it at first, the townspeople eventually convinced him to relent. Tosafot, citing Masechet Derech Eretz, comment that the ugly man was none other than Eliyahu Hanavi in disguise.
In another responsum (Teshuvot Tzitz Eliezer 12:43), Rav Waldenberg addresses the permissibility of undergoing elective surgery on a Thursday or a Friday. While the questioner was primarily concerned about the surgery interfering with Shabbat observance and enjoyment,⁷See Gray Matter 2 pp. 19-23. Rav Waldenberg simply responds that Halachah never condones elective surgery. If a surgery is not necessary, it may not be undertaken.⁸