Soo....the ML does NOT have black hair, but everything else fits. She has a limited time to live, has a "slave (? More like servant) has to count her steps, and her brother eventually finds out she is not his sister. Soooooo, maybe it is the one? https://www.mangago.zone/read-manga/happy_ending_for_the_time_limited_villainess/
This one? Not sure tho if 6 months living
But I think happy ending for villainess plot is also like that
https://www.mangago.zone/read-manga/when_the_villainess_loves/
Wait this one fits not sure about black haired ml tho hahaha https://www.mangago.zone/read-manga/death_is_the_only_ending_for_the_villainess/
its abt this girl that got reincarnated as redheaded villain that got poisoned and shes very weak and can see her system and only has like 6 months to live, like how many steps she has and shit and she makes a contract marriage with a black haired dude and she owns a slave that doesnt want to l ave her and she has a brother tjat knows she isnt his sister