I don't think she needs any antibiotics as it just doesn't look infected. If it is not growing in properly, something else is going on here. I think the only thing you can do is keep her healthy and living a normal life and see if it grows in. As long as she can eat and drink properly and seems to live a happy life, then let her be. If at any time she starts to go down hill or can't eat, you might consider putting her down.