What's the difference between 정형수술 and 성형수술?

ANSWER: One means "surgery (수술 手術) to repair the shape [of something]," and the other means "surgery (수술 手術) to make or form the shape [of something]." The word 정형 (整形) can literally translate as "to repair (整) a shape (形)," and 성형 (成形) can literally translate as "to make or form (成) a shape (形)."

If you break your nose, the surgery you need to repair it is 정형수술, but if you want to change the shape of your nose, the surgery you need to reshape it is 성형수술, though the guy in the video below is recommending that you get a broken nose repaired with 성형수술. The definitions can be a little confusing, but you just need to remember that the Korean phrase for "cosmetic surgery" is 미용성형외과 (美容成形外科), NOT 미용정형외과, despite the example in the definition for 정형 below, which is probably one reason many people get the two confused. The word 외과 also means "surgery." 

By the way, does picking your nose make your nostrils bigger?

ANSWER: No. You would have to pick your nose long and hard for that to happen.