If you are concerned about costs, you can do a breakdown of the average vacation cost for the region and then add on the surgery costs to that.
You could also look into getting a credit card to bring with you as a back-up. I have done this when traveling.
For plastic surgery in South Korea - you will need a valid passport, appropriate visa or K-ETA status (if applicable), and a confirmed appointment. As mentioned, most western tourists can enter without a visa for up to 90 days.
Checking Google reviews is helpful. I believe they are more strict with reviews when it comes to medical services.
At least that seems to be the case here in the US. I noticed that "fake" reviews or inflated stars does get removed.
You sound very small so I would imagine it would be on the cheaper side. Women that are lager tend to have extra costs as the surgery is a bit more invasive and recovery time ends up being longer.
Dr. Myung Ju Lee M.D. Ph.D offers this at his clinic and he gets very good reviews on Google. Check out him and see what you think. It seems his clinic offers various options as well for reduction depending on your needs or desires.
I am not entirely sure about this but you can look at the top-rated clinics and see if they offer this. I did see something about Korea looking to have hair loss be covered as a medical treatment instead of an elected surgery for Koreans which is pretty cool!