The central halachic tension surrounding elective cosmetic surgery runs through the Talmudic debate recorded in Bava Kamma 91b, where the Gemara notes a tannaitic dispute over whether a person is permitted to injure himself — with one view holding that it is not permitted and another holding that it is — establishing the foundational question of whether surgical alteration of one's own body falls under the prohibition of self-injury.
The Rambam rules decisively on one side of that dispute, stating explicitly in Mishneh Torah, Laws of Injury 5:1–2 that it is forbidden for a person to injure either himself or another, which becomes the baseline halachic concern any permissive ruling on cosmetic surgery must address.
Tzitz Eliezer 11:41 is not available in text for Mekoros to read, but our research indicates that he addresses a major responsum directly weighing concerns of self-injury and needless bodily alteration against benefits such as beautification, self-esteem, and social and psychological need in that source, making it the key authority for this question.
Tzitz Eliezer 12:43 is not available in text for Mekoros to read, but our research indicates that he addresses the conditions under which elective procedures may be permitted in this companion responsum.
Igros Moshe OC 4:79 is not available in text for Mekoros to read.