As she is having repeated episodes of vomiting child should be evaluated throughly by a Pediatrician. I s there any headaches
associated? any unilateral headache?
As she is adolescent , the vomitings occured during her mother absence other nonorganic causes like bulimia nervosa
and anorexia nervosa
should be ruled out by taking proper histiry and examination.
So better to consult Pediatrician