Anybody know of the manga/manhwa title where the female lead will cough up blood/faint jus...

I’m not sure but its kinda similar to https://www.mangago.me/read-manga/when_the_villainess_loves/

I'm pretty sure this is the one you're talking about https://www.mangago.me/read-manga/happy_ending_for_the_time_limited_villainess/