I don't think it's the Biogroom, of course, make sure you are rinsing the shampoo out thoroughly, it's highly concentrated, and you want to dilute it before using it. The conditioner is also concentrated, but it's not as important that you rinse every little shed out. Joey had a wonderful coat, but I love his new haircut, and maybe something like this could work for Uni, until you find the problem.
Itching can be tough to figure out, and sometimes you can eliminate the problem, but the skin is still reacting from all the scratching, which causes more itching. Have you talked with a vet about an anti-itch cream? I was also wondering about a homemade diet for short term, just to see if it was diet related. For children, they eliminate all but one or two foods, and keep a food diary, and each week add a new food. I believe that when we did a food switch with Joey, and he developed copious eye tearing, it wasn't probably one of the major elements of the food, it was probably one of the minor elements, but it caused an extreme reaction with him. Sometimes having more control on exactly what they are eating can help. Good luck.