My 2 year old bulldog Wilson goes through the exact same thing as yours. Running his face along the crate, smelling bad, itchy little bumps on his skin and fur falling out. Tested for mange but negative too. Vet gives him an allergy shot, medicated shampoo and Atarax but nothing seems to be very effective. In my case I'm convinced it is something outdoors like the grass or weeds. I noticed when the weather was rainy and cold I kept him inside and his allergies seem to subsided to where they were much more manageable. Fur grew back in and the smell faded. Now that is warming up and he is able to go outside again the allergies have come back. He starts chewing on his paws and I immediately wash them and spray them with a mix of salted water and alcohol. I have to wash his underbelly as well. The cause of the allergies is hard to pin down and all us bulldog owners go through a process of trial and error with dog foods. I am sure you will gets lots of good advice here. I feel for the caring bulldog owner because all we want is for our dogs to be happy and comfortable.