Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear about Lizzy.
How were ear mites diagnosed?
If it was just on waxy debris alone without looking at the wax under the microscope for mites then she may not have ear mites at all.
If she doesn't go outside and isn't exposed to other animals it would be difficult for her to get them as it takes close contact to pass the mites.
Sometimes cats with yeast, bacterial or even demodex mites will have dark waxy debris too, and their ears will be very itchy.
Any ear infection will make an ear itchy.
The Hartz product Ultra Guard ear mite treatment does have pyrethrins which should be effective against ear mites. But there are some ear mites that have grown resistent to pyrethrins, and those wouldn't die. As well cats are very sensitive to pyrethrins, and their use can lead to loss of appetite, vomiting, drooling, incoordination and tremors/seizures if they are exposed to high levels for a long period of time, or if they happen to be overly sensitive. Her nausea may be due to the ear drops.
I suspect that in the long run it may be cheaper to have her examined by a veterinarian and find out what you are dealing with, then treat appropriately. Even if this is related to ear mites I suspect that a secondary yeast or bacterial infection is present too, and your veterinarian will have much safer products to treat all of her problems.
For now I would use a gentle cleaner in her ears daily to remove as much of the waxy debris as possible. I like Oticlens.
Best of luck with Lizzy, please let me know if you have any further questions.