This is a dicey situation.
First, I'd stop playing musical proteins with the food. Many times, although the foods are interchangeable, meaning they won't cause digestive upset when switched, they will cause allergy problems. Your bully might do well on lamb or beef but not on chicken or salmon. If you find a food he does well on, stick to it!
Second, as for the blood allergy test, I considered this also for my bully who exhibited terrible allergy problems. It turns out, since they were developed for humans and not dogs, they tend to be wildly inaccurate and produce a lengthy list of possible allergens, most of which are difficult to avoid. The skin allergy test is the most accurate but very expensive.
Finally, it could be food allergies and I'd focus there first - but something wild like only 10% of canine allergies are caused by food. Like us, most are environment, so from pollen, dust, dander - and things that are hard to avoid. In that case, you'll need to explore some different options.
One question: what did your vet give your bully that cleared him all up? Just curious as it might provide a clue to what's going on!
I know this is frustrating so hang in there!