ya you should definitely shop around for sunnies. I personally don't find LV sunnies to be *THAT* amazing, but that's just me... Good luck shopping and here are some of my tips:
square face: go for round sunnies to soften edges
Round face: square/rectangular frames are better since they elongate the face, avoid horizontal frames such as the faux-semblants
Heart shape: I really like aviator styles (some people suggest against wearing this style tho...) cuz they bring more focus upwards instead of toward the sharper jaw
Long/narrow face: I like round/elliptical sunnies and wrap-around styles (Dior makes wonderful ones!)
Oval: woohoo! go crazy! anything'll do!
Of course, buy whichever pair you like! don't go by what I say!
