For dry chapped udders, bagbalm works great and is ok to put over the wounds...but if you put a little neosporin on the wounds first it will really help. Before you do this though, take a wet wash cloth and clean it off a bit. And after all this, take some horse fly spray and spray her down real well, but don't get it on the udder...it could cause irritation. This will at least help keep the flies away.
I personally wouldn't give antibiotics for this.