Of course also children can develop an anxiety disturbance, which can correspond to the symptoms of adults, with suddenly appearing fear attacks combined with different physical complaints.
Typically such fear attacks occur during special emotionally loaded phases (e.g. separation from parents, diseases in the family, problems at school). A careful examination of an experienced therapist should take place in order to exclude other diagnoses and causes (e.g. trauma) or physical causes.
A special kind of anxiety disturbance in children is the fear of separation. More information in German.