I have a problem with my hen?

I got chickens about a month or so ago. The rooster and the hen was already a month old and the babies I got were 2 weeks old which makes them about a month or so old. The little hen and rooster I got molted fine they have all their feathers and they look great, but, the other baby chicken I got after it molted it grew like the stem of the feather but no feather ever grew it is only on her backside and around her tummy and face. No feathers at all and when I looked at her today there is like purple dots all over her backside where there is no feathers. Should I be concerned and have someone look at her or will she eventually grow her feathers because she is looking kind of bad. Thanks please reply soon.