Ouch. That sounds painful. What is the desired effect from having injections under the eyes?
Actually Botox is not a "cosmetic surgery procedure". It is simply, an injection of botulism toxin placed into the muscles, thus "paralyzing" said muscles. It does not remove wrinkles and deep lines. It stops the muscles from forming wrinkles by not allowing the movements that create them, like frown lines for example. It may give the appearance of smoothing out existing wrinkles, but only because when contracted, those muscles under the skin no longer are able to produce a wrinkled appearance.
Please check the Asian Plastic Surgery Forum for answers to your questions about procedures and recommendations in Korea.