유난히 오늘 따라 왜 그렇게 웃고있는거니?
: why are you so smiling(at me) a lot today?
얼마 전 내게 ᅡ소개 시켜준?
: i guess this sentence could be "얼마전 내게 소개시켜준 (그사람/그남자/그여자 etc..)
if that, it means "(the guy/the lady/the person) you set me up with a couple of days ago.
"소개시켜주다" will be translated into Korean with two different meanings and it depends on context. when it's regarding "a date" between a guy and a lady, it could be translated into "set somebody up with somebody" like a blind date, also it could be "introduce somebody (to somebody)" make them get to know each other.