Many people who cut themselves try to explain it away by saying their cat scratched them. These could be cat scratch marks — if Demi was ever near a full grown tiger or lion. (!) Interestingly enough, Demi has been wearing long sleeves to all of her more recent appearances.
Demi, who had very little experience before being cast in Camp Rock, has admitted being bullied in public school to the point where she had to leave. Could she be finding herself overwhelmed by all the attention of suddenly being a teen star? If so, hopefully she finds the help she needs.