Is it possible for you to request a hair analysis to test for heavy metal toxicity?
My son has seen two different dermotalogists; his regular pediatirician; an oncologist; a speech therapist; and we are scheduled to see a neurologist and a child development specialist. He did have a complete blood panel done including liver enzymes about two months ago and everything came back normal. He just had a brain MRI yesterday and an ultrasound on his liver, now we are just waiting for the result
There is some thought that vaccinations in some children, particularly boys present in behaviors such as your child's. Skin rashes and liver enlargement hint at a toxicity issue, again it could be from vaccinations. Pediatricians say that thimerosal has been removed from vaccines, but that is not true. I would try to find a naturopath medical doctor who doesn't use drugs or surgeries to see if there is some kind of heavy metal toxicity or environmental factor that may be contributing to his problems. They can test hair and I'm sure the tests would be noninvasive to your son since he's so young.
Celiac disease (a disease characterized by the inability to digest gluten) can cause an itchy rash. It can also cause neurological problems, and, in occasional cases, liver damage. This is just a thought, prompted by your comment that your child has seen it many doctors and no one has come up with an explanation. That sometimes happens with celiac disease when it presents with atypical symptoms. (Probably the most typical symptom of celiac disease is chronic, oily/fatty diarrhea, but not everyone gets that.)
Another thought might be some other type of autoimmune disease that affects the liver.
Hope you get a diagnosis soon. Good luck.
You mention that your son has been evaluated by a number of doctors. What types of doctors have evaluated him thus far?