I Know exactly how you feel. I have a little handreared one at the moment, Tarka, and he has the constant runs. He is on antibiotics, pro-kolin and I have just got him some Lacto B. He is so very bright in himself, eating and drinking well but I have had to crate him as he just leaves poo wherever he goes. His bottom is just constantly a mess and if I bathe him, give minutes later he is filthy again. It's almost as if he cannot close his bottom, if you know what I mean.
The vets says if he does not clear up then next step is a stool sample, (more like a very runny sample).
I'm worried that it may be a physical problem with him that cannot be sorted and don't know what I am going to do, he is just such a happy little soul but, like you, I can't even cuddle him without getting covered and then I have to have a bath and change before dealing with any of the others.
Hope Toby gets better soon.