Drama/Movies where Older Sister takes care of Little Brother

• Jealousy Incarnate
• Uncontrollably Fond
• The Princess Wei Young (her fake half brother)
• Come and Hug Me (her adopted brother - they are close but he looks after her more)

These probably aren't what you're looking for, but these are dramas where the family relies on the FL, including her younger brother, or the FL tries to protect her family from danger, including her younger brother:

• Sungkyunkwan Scandal
• The Hymn of Death
• About Time
• The Rise of Phoenixes

Oh My Ghostess

Movies:

1. Bad Sister 
2. The Third Way of Love 
3. Bunny Drop 
4. Our Little Sister 

Drama:

1. Drama Special Season 6: Live Shock 
2. Back to 1989 Not the focus of the story
3. Bromance Not the focus of the story
4. The Perfect Match Not the focus of the story
5. Seo Yeong, My Daughter 
6. Stars Falling From the Sky 
7. Take Care Of Us, Captain 
8. The Bridal Mask 
9. The Master's Sun  Not the focus of the story
10. I Cannot Hug You  Not the focus of the story