So sorry to hear about your kitty. Years ago, I had a kitty (Lily) with this difficult and hard to treat skin disorder. At four months of age she developed the linear plaque on her hind legs. Soon followed the ulcers on her mouth and lips. One time she even chewed her own pawpads. After years of conventional medicine, which only relieved the symptoms temporarily, I took her to a homeopathic vet. They prescribed a home made diet and homeopathic medicines. Unfortunately, she was now older and never adjusted to the home made diet. I was lucky enough to find the Innovative Feline Diet canned food from my regular vet. They have food with a protein not found in most cat foods; i.e., duck, rabbit and venison. The homeopathic medicine helped somewhat but after years of being on and off of cortisone shots, her immune system was pretty weak. She was irritable, aggressive (she would attack me and my other cats) and pretty miserable most of the time. However, Lily had other problems too. I've seen cats with this disorder whose symptoms are managed very well and live an otherwise very heathly, long life.
A recent addtion to my kitty family, Mia, also has this disorder but I've always treated her holistically after learning from Lily. She eats a premium canned cat food (lamb is the protein) that has no by-products, artifical flavors, colors or preservatives. Her bowls are porcelain and are washed after every meal. I don't leave food down for her and she never eats dry food. And no corn or wheat. These are known allergens. Things to look for in a canned food are: no by-products; high-quality meat; whole grains and vegetables; omega-3 fatty acids (which will really help with this skin disorder). This month's The Whole Cat Journal has a very good article about canned food and lists some of their top choices, Azmira and Felidae being two that are particularly good for kitties with allergies.
Your vet is correct in trying to get rid of anything plastic. I would also be careful of toys that may cause a reaction. And stay away from cortisone shots. They will only weaken her already compromised immune system. Try building her immune system up with vitamins and whole, natural foods. Anitra Fraiser, author of The New Natural Cat has some very good information concerning this. Good luck to you and your kitty. I hope this has been of some help.