for example: miss no good (drama) has very amazing makeover hi my sweetheart (drama) guy have amazing makeover (girl has a little makeover too) 200 pounds beauty (movie) ! amazing plastic surgery transformation full house take 2 (drama) ! tada, kimi wo aishiteru (movie) !
Well a new drama called She was Pretty, is really good I myself couldn't stop watching it. It will take a bit of time for her transformation but it is big and it is worth it. And the humor, secrets, and romance keep you wanting to watch it. But trust me it is a must see. Oh and another transformation one is called Princess Hwapyung s Weight Loss, or something like that but that is really good too. I hope you enjoy at least some of these.
Ugly girl becomes pretty:

Perfect Match: she has an acne situation
200 pounds of beauty: well title says it all

Shy/doormat girl becomes stronger:

Fated to love you (Korean version is better): her shyness and weakness for some reason come out as strength and not annoying at all.
Miss no good: fashion terrorist lol
Nadeshiko Shichi Henge: she has a trauma and is weird making her super closed up
To get her: Momo is super shy
she was pretty it's still airing but you should give it a try 
flower boy next door : she was having social phobia 
birth of a beauty is a good one
She was pretty is literally what you just described!! I also like Fated to love you Taiwanese version
Korean drama "Love Tastes so Sweet" (aka Snow White) or the k-movie 200 pounds beauty.
"Oh my Ghost" it starts with the female lead being very shy and awkward and shows how it can be a problem, then she is possessed by a ghost of completely opposite personality (which is also a bit too much) and by the end of the series she matures and achieves a good balance between shy and outgoing. 
Birth of a Beauty
She Was Pretty
Oh my venus
Snow White
Marriage Not dating, Playful Kiss