Very itchy skin in sweet rescue dog

Hi- I am hoping someone might be willing to help me with my sweet little rescue dog. I have had her for about a year, but I do not know any of her prior medical history. She is a Pekingese who appears to have had puppies at some point in her life. The vet believes her to be about five years old.

When I first found her, I noticed she was a bit slow and seemed to tire easily. She would bite the base of her tail and haunches until they bled. A crusty scab would then form, which she continued to bite. Her skin has also turned black in her ears and along the base of her spine/ back.

I believe she is allergic to fleas, which I try to control naturally. However, it is winter here and there are no fleas to be seen, but she is still scratching and biting herself in the same areas.

Additionally, she has a thick, yellowish green goopy discharge from both eyes.

She is on a diet of raw chicken or turkey, as well as brown rice/ quinoa and veggies (broccoli, peas, green beans, or leafy greens). I give her cod liver oil and a special canine probiotic daily. If she strays from this diet, she has bouts of diahrrea with occassional small bright red blood streaks. I have seen her energy and coat improve since I found her and started this regimine.

I have tried all sorts of things with her- ACV, coconut oil, oatmeal baths, flower remedies. These things have helped some but have not resolved the problem, and she continues to be in misery with this scratching.

The spots are very hot to the touch. She will allow me to touch the spots and even stop her from scratching. She is a mild mannered, friendly, easy going dog. Nothing seems to bother her except the vacuum cleaner. She has a great appetite and eats anything. She also snores a lot, but I believe this is due to her breed.

Thanks and blessings to anyone who will help May and me.