Breaking out in hives is an expression describing an allergic reaction on the skin that produces blisters. http://www.google.com/url?sa=i&rct=j&q=&source=images&cd=&cad=rja&docid=GELkRJ7m0aSyRM&tbnid=YXFdnRRPXzN2kM:&ved=0CAUQjRw&url=https%3A%2F%2Fwww.healthtap.com%2Fuser_questions%2F629154-i-had-an-allergic-reaction-to-biotin-5000-mcg-i-broke-out-in-hives-on-my-arms-and-i-was-taking-them-to-help-my-hair-what-can-i-do-so-i-can-take-them&ei=ulCvUfrmJoysqQHI7IHoBA&bvm=bv.47380653,d.aWc&psig=AFQjCNE9xv3DSFZ5UjpuxMNw42pcgO3FCQ&ust=1370530350853137

The primary meaning of "break out" is to begin or arise suddenly.

To "break out," alone, can mean to break out in acne (to suddenly develop pimples or pustules on the skin). The author is specifying that "she broke out in hives," meaning that she is experiencing the onset of a skin rash.