Yes, it is okay for a Christian to get cosmetic surgery, but it should be for the right reasons. If a person is very self-conscious about a physical aspect of his or her body and it is causing emotional or even physical discomfort, then cosmetic surgery is certainly an option. However, if a person wants to have surgery so as to enhance something for the reason of being more attractive, then that can be potentially wrong. Let me clarify. There's nothing immoral about wanting to be attracted to the other gender as long as it is a godly desire. Perhaps a wife wants to have things "fixed" so that she can be more pleasing to her husband (if that is important to him). Then, that could be an option. On the other hand, some women are quite self-conscious about things like "small" breast size, where others are not. If the woman is overly self-conscious about it, then breast augmentation could be an option. However, if a person wants cosmetic surgery for the purpose of becoming more sexually attractive simply for the sake of becoming more sexually attractive, then that is not morally justifiable.
In that case, corrective surgery for a deformity, injury, or medical necessity could easily be justified. There are women who had mastectomies and have had implants to rebuild the breasts. This is certainly acceptable. There are people who are not happy with their noses, which might be causing them embarrassment and/or insecurity. There's nothing wrong with considering corrective surgery to help in that area.
There's also corrective surgery for the sake of health. Sometimes cosmetic surgery can enhance the quality of a person's life by making the person's ability to breathe better, walk better, talk better, etc.
My own daughter has had a kind of corrective surgery where a bar was implanted in her chest (pectus excavatum) and manipulated so that her rib cage is now expanded. The cosmetic result is an enhancement of her chest size. But the real reason it was done was that her particular condition was causing about a 15% loss of lung capacity. So, cosmetic surgeries are certainly justifiable when they are for the improvement of physical health.
Likewise, cosmetic surgeries can be justifiable when they are for the improvement of psychological health. Each person is different. Security and insecurities vary between individuals, and there are so many variables that each person should consider her particular situation with care and Godly wisdom.
For the most part, Christians should be satisfied with what God has given them at birth. But this does not mean that a Christian should be satisfied with a deformed arm, cleft palate, or whatever else might be in need of correction or improvement. Different people have different issues they need to deal with, as well as different abilities to cope with them. If cosmetic surgery is done for the purpose of enhancing physical, psychological, even emotional health, then I can see nothing wrong with it. If, however, it is for selfish reasons, for the attention, for the sexual attractiveness simply for the sake of being more sexually attractive, these are selfish reasons, and that is not biblical.