医院

English squashes both ideas into 'in the hospital,' but Chinese splits them by your role. 在医院 marks location only: you could be visiting, working, or waiting in line. 住医院 means you are checked in as a patient and a bed has your name on it. Spoken Chinese normally shortens that to 住院, so 我妈住院了 is what people actually say. If a coworker tells you 我在医院, ask which one they mean before you send flowers. “休息两星期， 七天住医院 医生人很好， 房间大漂亮。” (I rested for two weeks, spent seven days in the hospital. The doctors were very nice, and the room was big and pretty.) ── [《一二三 住医院》](/read/hospital-days-pricey-plates#s2)

家 literally means home or family, and Chinese reuses it for institutions that run under one roof. Banks, companies, restaurants, hotels and hospitals all take 家. The generic 个 is for loose objects, so 一个医院 sounds like a foreigner counting cardboard boxes. In news writing you will also bump into 一所医院, which is just the formal twin of 一家医院.

看 means to look at or to visit, and its target is normally a person or a screen: 看医生, 看朋友, 看电视. A hospital is a destination you travel to, so the verb has to be 去: 去医院. Natives often chain the two ideas together, saying 去医院看病 or 去医院看医生. Say 看医院 only if you genuinely mean standing on the sidewalk staring at the building.