Facebook search question?

[Jane D]

You know when you search someone on facebook over and over even though there not in your friends list and have no mutual friends with them what so ever so there like a total stranger and then when you write in the letter there name begins with it comes up? well if i use a different computer will that still happen or will it only happen on the computer im using now as i searched someone i shouldn't have on by using my sisters facebook lol long story but we have separate computers so will that only show up on mine?