one's own room
Refers to a person's private room, often in a shared living situation like a dormitory, hotel, or family home. Slightly formal; in casual speech 自分の部屋 is more common.
He is shut up in his room studying.
At the hotel, I relaxed in my own room.
He shut himself in his room all day to study.
I like listening to music in my room.
After finishing dinner, she went back to her room.
個室 refers to a private room in a facility like a hospital or restaurant, whereas 自室 means a person's own personal room at home or in a dorm.
Compound of 自 (self) and 室 (room). A straightforward Sino-Japanese word.