What about zinc applied directly on the skin?
I second castor oil as well, everybody loves coconut oil but it is such a light oil it really does not have as strong of properties as your heavier oils, including olive and hemp seed. I have always used a calendula and plantain infused olive oil or castor oil for Everything.
calendula is a strong anti fungal as well as a very soothing healer. Plantain is a strong anti bacterial and healer with anti inflammatory properties.
I am not sure if zinc applied topically on goats is safe but if one of mine were in that situation I would use a topical zinc diluted with an infused castor oil. That will help soothe and heal. Of course in conjuction with the injection of ivermectin for mites.