I am sorry to hear about your encounter with tea tree oil. Normally your chances of a reaction to it would be more than one chance in 10,000, or maybe it is some other chemicals that are in the product that cause the problem. Who knows? The main thing for now is you've got the symptoms stopped. As BARKINGDOG mentions be careful of natural products. Just because they are natural products and work well for us and our dogs and horses, some can be extremely dangerous for cats. Cats' metabolisms and immune systems are so delicate to chemicals compared to ours. Inadvertently using products that are great for us can raise havoc with the cat system. The rule I have had to learn is if I don't know I don't use it, either research it or find someone in the know and talk to them about the product. This can save being schooled in the school of hard knocks. Remember the pet supply company is out to make money, and it's a case of buyer beware.
What name does your cat go by? It would make it more pleasant to refer to her by name than just (she). LOL. Anyhow considering it appears to be a skin condition, I would be just checking the toxicity of my cleaning supplies, and the method in which they're used to see if this could be adding to the problem. I realize the cat is under extreme stress from the FHS but is there anything else in the apartment that could be stressing her out as well for example, strangers coming in that the cat is not accustomed to, kids roughhousing with her that she's not appreciating, and I realize you are under extreme stress from the situation, and the cat will pick up on that as well to add to her anxiety. They even pick up on family squabbles between different members which doesn't help either. Fragrances in the way of air fresheners and perfumes in bodycare products not to mention the litter box can all add to the problem under certain circumstances. Also stay away from prescription drugs if at all possible especially if they're being administered on a trial basis to see if it will help. Depending on the drug they too will help to stress the animal.
For the time being I think I would stick with the product that you know will work to relieve the symptoms, and try her on coconut oil in the food. Start small - a spot about half the size of a pea or 3 to 5 drops if you want to warm it up and use an eyedropper with feedings night and morning - slowly increase the amount over 3 weeks to a month to where she is getting about half an eyedropper or maybe more. I have found that amount to work well for me. It may be different for you. Take your time with it you don't want to stress her with food change. I read somewhere that it can be applied externally with good results, I haven't done this as yet, but it might be worth looking into. Also find some toys that you can interact with her in a playing session 2 or 3 times a day. It will help to take her mind off the problem.
Look forward to hearing how things are going.
Animals are such agreeable Friends.
They ask no Questions. They pass no Criticisms.