hi and welcome to HCM ,
Moderate to severe attacks of headache can be neurological pain seen in MIGRAINE
since the girl is young and is we cannot expect tension or stress
related problems in her to be the cause of headache.
Headache due to tension applied by Orthodontic wiring or braces is rare and no orthodontic tension is applied by elastics which is low tension used for tooth movement .
Yes it can be psycological feeling of a patient to experience such pain.
so you can try removing the braces and check if the headache is relieved .
or else i would suggest you to consult a physician and get the examination done who can come up with exact diagnosis and treatment plan .
i hope this information is satisfying.