No need to use essential oils on pets, no need to risk it. Flowers of Sulphur is an excellent ancient remedy which is very cheap and easy to use. It is actually very healing for the skin, never harmful, just the opposite (good for so many ailments, worth googling).
Sprinkle it with a flour sprinkler on floors, bedding, pets, repeat as necessary.
We had a very warm spring/ summer in UK this year and I had fleas first time ever on my house cats and it quickly turned into a huge house infestation! However, FOS seemed to have worked immediately, eased the itch as well. I happened to have FOS at home as my husband uses it for his psoriasis.
I hope it helps, I was devastated when I realised the scale of infestation but after a thorough vacuuming (vacuum some FOS to kill the ones in the bag) and sprinkling all seems to be fine now.
I also put a piece of amethyst in their water bowl as I like the sound of it :)
The vets prescribe very dangerous chemicals, which are proven to contribute to feline cancer.
Best wishes everyone.