A couple things could cause this other than allergy. Since she got braces, the shape of the outside of her mouth has changed, such as her lips stick out further than they did before. It probably feels weird to her, makes her more self concsious. She may be licking her lips alot more than usual. This causes peeling and chapped lips.
Another possibility (and the most probable) is that she is brushing her teeth more than she ever did. All that brushing is taking the natural oil that keeps your lips moist right off her lips.
Since she can't go without brushing (as that would defeat the purpose of the braces
) she'll probably just need to keep her lips moisturized throughout her braces experience.