Hello, 

I'm looking for recommendation of dramas where female character is sick, has a fever, faint, is injured. 

Can be any genre. 

Thanks for any recommendation! 

These came in to my mind:  well intended love, doom at your service, crazy love, marriage contract.

I would put this last, after other suggestions but Boss & Me involves the male lead's sister being sick and the female lead being a donor for her.

I can't say I remember moments like you describe because it has been years since I watched it but it's possible there are some given the story and plot - surgery.

It is very common for either or both the FL and ML to become sick, injured, etc. Like in historical dramas they get poisoned, or stabbed, and become very sick, but always recover.

count your lucky stars.  FL faints 2 or 3 times