Studies show that nondisplaced (broken but not separated) clavicular (collar bone) fractures do just fine with a simple arm sling. The figure-of-eight brace is no longer recommended. It was uncomfortable and didn’t change the final results.
The type of sling you saw to hold the arm down by the side is more for people who dislocate the shoulder anteriorly (in a forward direction). It keeps the arm in a position of external rotation, which evidently improves the results. The simple arm sling you have left of the three choices is no longer considered a good choice for anterior shoulder dislocations, but it is recommended for fractures of the clavicle.
When applied properly, it takes pressure off the collar bone while healing takes place. In a young teen, healing should take place fairly quickly. Your pediatrician will continue to monitor her progress and let you know when the sling can be removed. Repeat X-rays may be taken to evaluate the progress of the bone healing.