The writer of that sentence is not a Korean and The sentence is not a proper Korean. I guess he meant "숨넘어가는줄 알았네" which means "I felt that I might be breathing my last" (because of a tight turtleneck.)

There is no expression like that. Isn't it '목 빠지는 줄 알았네'? It means 'I was really looking forward it'.