What kind of dr are you seeing now? An endocrinologist or gastroenterologist? A standard allergy test will not be sufficient when those numbers exist. We are in the same boat right now, with the IgA deficiency and several other numbers that are either low or high. We've been referred to both endocrinology and gastroenterology, and my child has a colonoscopy and intestinal biopsy scheduled soon.
I am not suggesting that your child's problems are the same as mine, but my child's doctor is thinking Celiac disease or another autoimmune disorder. But first you need to make sure you're not seeing a regular pediatrician, but a specialist, probably in gastroenterology.