I am sorry you are going through this. Please know that I am not a doctor or a dermatologist. My first suggestion is to get another opinion from a dermatologist.
The burning skin symptom does ring a bell however with a post I wrote about Periorial Dermatitis. I don't know if your doctor offered this as a possibility? Are you using any new moisturizers or skin care products? Do you use fluoridated toothpaste? Are you using corticosteroid creams? Do any foods seem to aggravate your condition like spicy foods? What happens if you just wash with water...no soaps or facial products?
Your skin condition could be any number of things so it would be a good idea to seek the advice of another doctor to make sure of what this is and how to treat it.
Please let us know if you find out what is causing your skin irritation. Thank you for your question.