Dokuzu na Kazoku to Wakareru Houhou: Tensai no Ane wa Jitsu wa Dame Onna. Munou to Iwareta Imouto wa Kyuukoku no Madoushi Datta

Abused by her family, Noel was almost killed by her older sister, which led to the development of her magical talent and the ability to cast barriers, which saved her from death. To escape her abusive family, she applies for a scholarship to live in a dormitory at a national school, but the skill she demonstrates on the entrance exam, 'putting protectors on eggs', will change her destiny... https://www.cmoa.jp/title/267153/