I've watched a few k-dramas where the girl was introverted but she was also rude and insensitive... are there any kdramas where the female lead is introverted or shy and kind? 

If you are looking for a introverted shy kind girl who eventually develops a stronger character, try "Oh My Ghost", "Kimi ni Todoke", and "Nobuta Wo Produce".


Flower boy next door is about a girl that is so afraid of social contact that she doesn't leave her apartment, she is nice in my opinion. 
Monstar
Heartstrings
:)
I've watched both Flower Boy Next Door and Heartstrings :) They were pretty good.
I second Oh My Ghostess.
49 Days, Heart to Heart
Fated to love you
I am currently watching "Flower Boy Next Door" and the lead in that is great.