FL loves SML first

 Sangmo:

She then realizes her love for the ML, but has to win his love because of how she treated him

I'm afraid I can't think of any dramas that fulfill this criteria exactly. 

 Sangmo:

dramas where the FL loves the SML and stings along the ML for awhile. She then realizes her love for the ML

 Sangmo:

Japanese or Korean please

Dramas where the ML likes the FL first while the FL likes / is interested in / dates or has a relationship with the SML well before she realizes her feelings for the ML:

• Korean
  • I Hear Your Voice 
  • I Need Romance 3 
  • Witch's Romance 
  • Empress Ki
  • Romance Is a Bonus Book
  • Dream High
• Japanese
  • Kimi Wa Petto / Kimi wa Petto
  • 5-ji Kara 9-ji Made
• Chinese and Taiwanese (Some of the best examples of this trope IMO) 
  • Sound of the Desert
  • The Story of Ming Lan
  • My Fated Boy 
  • Story of Yanxi Palace
  • The Legends
  • In Time With You
  • The King's Woman
  • Before We Get Married

Moon Lovers korean drama (it's historical drama)

Kimi ga Kokoro ni Sumitsuita This could fit. How she treated him is hesitating between him and the 2d ML and being very confused about her feelings. This is more compelling than the usual love triangle. There's a little twist (hint: it's about self respect for both leads). 

Maybe I Hear Your Voice but I put it on hold so I'm not sure. There's a love triangle and I know the FL is not very nice so it might fit. 

The Spies Who Loved Me she is not very nice to him for a time, but really she was justified and they both know it. I don't think she really has to apologize. 

I agree Chinese and taiwanese dramas are more representative of this trope. If you're interested let me know.

 starflakes:

The Japanese movie Daytime Shooting Star sounds like it'd mostly fit this. I don't think the FL really has to work to win his love, but it is a drama where she likes the SML first. 

actually thats the trick. the one you are calling sml is the ML. and she liked ml first not sml. she just ended up with SML.