Warnings on Tea Tree Oil and other related products - for cats.
Using Tea Tree Oil topically on a cat.
Tea tree oil, which contains phenols (as does its neighbor, turpentine! ) is very toxic to cats because they do not possess the enzymes to metabolize it, so it is stored in the liver and can cause irreparable damage over time.
Most veterinarian medicines are prohibitively expensive, harmful or outright poisons. If health is a business, let the buyer beware. However, I would see a vet just to determine if the cat has also an ear infection as well as ear mites. Antibiotics have a long-term damaging effect on the body and some cats do not recover well at all.