Pretty sure this happened in Dr Slump especially when they were in school, tho maybe they “only” fainted??

FL in Vivid Romance (A romance full of life) suffered from nosebleeds because she was studying hard and part-time working, barely eating and very stressed.

Someone at DB is *living in my head*!!! Out out begone before thou see-est all my secrets ;)
I was literally just thinking about this yesterday after watching Hagwon Romance... Like, so many people in Kdramas need to get their Blood Pressure checked stat!! How, and why, do they bleed so easily? I'm a person with high BP and very easily stressed but I've never had one in my life touchwood.
As to the treasure hunt, I know there are *many*, which prompted my ponderings, but off the cuff, can't remember any other than the aforementioned, sadly.

Where Stars Land and I think just about every drama set in a high school or college

Every overworked character (student or adult) in Kdramas.

As an example, I remember the teacher, Sun Woo-Young (Oh Man-Seok), in What's Up. It had a sad meaning in his situation 😥

Not a drama but a movie: Exhuma. Kim Go-eun got a nosebleed from a vengeful spirit.

In you who forgot poetry / a poem a day - I'm not sure whether it was bo young or the crocodile t-shirt guy (shin jae Hwa) who got a nosebleed. But it was due to their work stress. One was almost homeless and the other was worried about their job security. At least I think it was.

This is too common that I can't remember it all. But I think Deok Sun's nose bled in Reply 1988. A bit hazy on the reason maybe school related.

In the old days of kdrama, a nosebleed was a sign of impending cancer (to the point that it was parodied) 😁
My favorite nosebleed was in Kim Sam Soon but it can’t count here because it was due to some (very) physical activity 😉

I'm pretty sure I saw this in Lie to Me, studying for the civil service exam.

Because This Life Is Our First, episode 6 - the ML gets a nosebleed during his hastily-arranged wedding with his contract wife. He says getting married so quickly was as chaotic as if he'd been beaten up.

I think the FL has one in Another Miss Oh. Can't remember specifics, though.

Every school/college kdrama ever, or just about any other show that has a character who is shown even very briefly studying, sageuks included.

"Semantic Error": Chu Sang Woo gets a nosebleed when he is continuously prevented by Jae Young from doing the things that makes his everyday as a student possible, his own ways of accommodating his neurodiversity.
It's a lovely film, but knowing what struggle it really is for a neurodiverse student to make a day work in a neurotypical environment, it was hard to see that part. One's laugh stiffens.

I guess it is easier to count the ones without a nosebleed. Having said that I have never seen a stress induced nosebleed in real life at all. So, it is either living in Korea is super stressful.

Castaway Diva
Episode 10
Yoon Ran Joo was working on a song for Seo Moh Ka

I think the FL had nosebleed from overworking in Boys Over Flowers.

Sweet Home, although in that one the nosebleeds are a bit different than the usual trope.

On the sickly / overworked trope though, I've never seen anyone in real life collapse and be taken to the ER for a quick nap and IV fluid drip. I can't decide whether these drama characters are malnourished, overworked or both.