If it is indeed mites, then oral ivermectin or moxidectin will generally work. However, there is the chance that they won't if you are dealing with the biting rather than the sucking lice.
You have to dose for 3 doses 10 days apart to break the life cycle.
If you haven't actually seen the mites, then you would do well to have your vet do a skin scraping and fungal culture just to be sure what you are dealing with.
Licensed Veterinary Technician