Historically there have been few psychiatric studies into fame, possibly because it's very difficult to recruit celebrities to be part of experiments. In the past it was thought that the kind of personality who pursues and attains fame may be one predisposed to psychological problems, possibly narcissitic personalities exhibiting self-absorption, egocentrism and self-importance. Yet some recent research suggests that it is the effect of becoming famous that is the real psychological hazard, not the personality type. Research by Mark Schaller proposed that famous people may be more self-conscious and self-obsessed as a result of the increased public attention they face. He argues that the heightened self-consciousness and introspection may trigger mental illness.
Most people would feel self-conscious entering a room if everyone turned around to look at them, and famous people experience this all the time. Schaller argues that famous people have difficulty reducing expectations on themselves and try to live up to unrealistic ideals, possibly imposed upon them by celebrity fans and feel increased pressure to live up to perfection.
The bottom line in the research is that excessive attention may not be good for you, especially when young.