A childhood belief about sleeping

At some point when I was little, I had some eye-related illness, and there was one time when my eyelids got sort of glued together. Because of that, I was afraid to keep my eyes closed too long for some time. But I knew people slept with their eyes closed. So at night, I would periodically close my eyes for a short amount of time, thinking that it would be enough. I remember some dreams from that time, though, meaning that proper sleep eventually set in.