I've seen (I'm in charge) Singapore 

Innocent Man 

Heart stings 

Princes prince 

 I don't care what country iNO INCEST PLS! but I like protective brothers who take care of their little siblings 

Some Japanese ones : 
- Namida wo fuite
-Wakamonotachi
- Himitsu no Hanazono
- I wish (movie - kind of)
- Rinne no ame (special)
- Ryusei no kizuna
- Saikou no jinsei no owarikata
- Youkoso, wagaya e

the following ones doesn't involve real brothers and sisters but has the same kind of relationships :
- Engine,
- Kazoku no katachi
In Jealousy Incarnate the female lead has a younger brother that kind of takes care of her rather than she of him lol but he is just a side character.
Rebel, thief who stole the people has a male lead who is the older brother to a younger sister, I think.
I Remember You has a focus on two brothers......buuut it's kind of.....well...difficult.
Plus nine boys is about a bunch of brothers but I don't remember if they actually interacted a lot with each other....
The male lead in Moonlight drawn by clouds has a younger sister which I think he is also somewhat protective of.
Hey, Goblin actually had a younger sister that he was kind of protective of! Okay, now I'm grasping at straws. Surprisingly difficult to find....your safest bet for sweet family moments of any kind are usually family dramas. There will be plenty of sibling relationships to go around. I'm not really well versed in those though, I could only really recommend: What happen's to my family and second Panda's recommendation of Five enough. 
Sorry, I did my best to find some.
Angel Eyes - It's the reason the male lead leaves for 12 years at the beginning.
Yamada taro monogatari
Yasuko to kenji
Jealous incarnate
The Moon that Embraces the Sun
Kill me heal me
Stars Falling From the Sky

Elder brother and younger sister:(Korean drama)

Just between lovers 

Scandal 

Spy

Lobbyist 

Giant

Goodbye Mr.Black

Prison Playbook

Sweet stranger and me(2nd lead has a half sister whom he's kinda protective about)

Discovery of romance(they meet at an orphanage and he's very protective of her-drama as a whole is crap)

Shark(beautiful sibling relationship.)

✔️ Reunited Worlds 

✔️ My Annoying Brother 

✔️ Hello Monster ( in part of the show) 

✔️ Scarlet Heart Ryeo ( parts of show) 

✔️ Hwarang ( secondary character takes care of brother) 

✔️ Ruler: Master of the Mask (2nd lead male during beginning of show) 

✔️ Lookout ( step- brothers) 

Adding to previous answers:

- Ugly Alert

- I'll Give You The Stars and The Moon (KBS weekday drama)

- Happy Together (1999)

- Legend of Orpheus

- Yong Pal

Except for a few, every kdrama has what you asked for. So, just pick any drama of your favourite kdrama actress and start watching it. Poor the lead, they'll always have a sibling to take care of.

I'm watching Come & Hug Me and it fits what you're looking for very well!

These are my favorties: 

East of Eden (this is the best thing I will ever watch in my life. Really really reeeaally sad tho but the best! It is a must watch)

Wakamono Tachi (All about my siblings): Is is the best Japanese drama with the best actors ever <3 This is a MUST WAAATTCH!!!! <3

Rinne no  Ame

My annoying brother

Brotherhood of war (Taegukgi)

Brother Beat

Endless Love

  • +1 to Come and Hug Me | Oldest brother/Younger Brother/Youngest Sister + Older Brother / Younger Sister
  • +1 to Just Between Lovers | Older brother/Younger sister & Older brother / Younger "adopted" brother

In addition: 

I'm using red for the protective character. If both are red, it's because they are protective of each other. If one of them is in bold, that's because that character is even more protective than the other(s).

  • While You Were Sleeping | Older brother/Younger Brother
  • Hello, Monster | Older brother/Younger Brother
  • Kill me, Heal me | (Twins) Brother / Sister
  • Another Miss Oh | Oldest Sister / Older Brother / Younger Brother
  • Oh My Ghostess | Older Brother / Younger Sister
  •  Soul | Twin Sisters + Older Brother/Younger Sister
  • King2Hears | Oldest Brother / Older Brother / Younger Sister
  • The Crowned Clown | Older Brother / Younger Sister
  • Cheese in the Trap | Older Brother / Younger Sister
  • Devilish Joy | Older sister / younger brother & sister + Older Cousin / Younger Cousin (practically brothers).
  •  Fight for my Way | Older Brother / Younger Sister (this is a small part of the drama, though)
  • Gu Family Book | Oldest Brother / Older adopted Brother / Younger Sister
  • It's Okay, that's Love | Older Brother / Younger Brother
  • Mirror of the Witch | Older Brother / Younger adopted Sister
  • Moon Lovers Scarlet Heart Ryeo | Older Brother / Younger half-Brother
  • Pinocchio | Older Brother / Younger Brother
  • The Smile has Left Your Eyes | Older Brother / Younger Sister
  • The Third Charm | Older Brother / Younger Sister
  • Weightlifting Fairy Kim Bok Joo | Older Brother / Younger Brother
  • +1 Hello Monster / I Remember You - I agree, it's complicated
  • +1 Just Between Lovers
  • +1 Come and Hug Me - step siblings and (in a less obvious way) blood related siblings 
  • +1 The Smile Has Left Your Eyes (although the older brother is very difficult to like, and also he's her adoptive brother - almost more like her adoptive father)
  • Bromance - the ML takes over the family business and looks after his mother and younger sister after his adoptive father disappears
  • Thirty But Seventeen - technically it's an uncle / nephew relationship, but they're so close in age that it's more like a brother relationship; they're closer in age than the "brother" and the FL in The Smile Has Left Your Eyes
  • My ID is Gangnam Beauty

Le coup de foudre Twins but he's the older one and their family brother and sister relationship dynamic along with their whole dynamic of portraying love -romantic and familial love is praised many people loved the family part of it go check it out!