In a passage near the end of Chapter 12, Turtle says that Sydelle Pulaski only uses her crutch as a means of getting attention.  Angela says she believes that Turtle means that it is Sydelle's way of hiding who she really is because she, like other people, is afraid of revealing that.  Sydelle thinks Turtle's crutch is her "big mouth" but Angela thinks it is her braid.

We are not told exactly what she means, so we have to figure it out ourselves.  We have to try to determine what it is about herself that Turtle wants to hide.  I believe it is that she is jealous of her sister.  Their mother gives all her attention and affection to Angela because she is beautiful.  I believe that Turtle's braid is meant to be unattractive and unfeminine because she feels that she cannot compete with her sister's looks.  Because she is worried about it, she reacts by making like she doesn't care about how she looks.  This is why she always wears the braid.