Is the woman who asked the question considered sinful for not telling anyone about her sister's cancer, based on the sister's request?

Medical treatment is permissible and commendable, and it may even become obligatory if abandoning it leads to destruction, based on the Almighty's saying: "And do not kill yourselves" and "And do not throw [yourselves] with your [own] hands into destruction." If an illness leads to destruction and treatment becomes obligatory, then the questioner's concealment of her sister's illness and her failure to inform her family constitutes aiding in the abandonment of an obligation and surrendering the patient to destruction. This is a sin that necessitates repentance to Allah.