Sadly it's warm out again, and the mosquitoes have somehow fallen back inside my home againGreat!
Essential oils are dangerous when consumed. Even trace amounts on our skin that gets on our fur. You should be safe with showering.
Our elder cats lived with us for over a decade each and we've used essential oils for various things. They've had/have blood work each year with no issues because of washing before touching them. We even have a diffuser that's kept out of reach.
At 16 (almost now!) and 19 they had what was considered excellent kidney and liver values. I know many other pagans in similar situations. I'm convinced that the studies haven't consist there still being trace amounts on the humans, getting on to pets.