Weird sick goat question?

that is totally wierd. I would try supplementing with some form of oil maybe some horse bran and flax seeds? put a tsp of baking soda in the water and make sure she is getting enough salt and mineral from her mineral block. seriously wierd though. the oils from the bran and flax will probably pump up the coat works for my horses and la mancha goats. also maybe try using an iodine shampoo to make sure her coat doesnt get infected if she is scratching. if it is too cold for a bath just spot clean her with it. good luck though seriously and post an update poor goat