Oh sorry to hear about your bully baby!
My question is this.... why oh why, if your bully has no food allergies, would he be on a limited ingredient formula? My understanding is that there is not too much of any one ingredient in this food, and a combination of many diff. protein sources.
I am looking at the ingredients- and I would not feed this, as potatoes are the #1 ingredient- which can actually lead to yeast problems. LI formulas are made for bulldogs who DO HAVE food allergies- so if you dog does not- get on something better that will enhance the coat, boost the immune system, and improve the skin!!
Step #1 would be to add salmon oil asap, any dog with allergies should have salmon oil- it helps their skin in so many ways!
Try a different food, if you don't like it, you can always go back

This food has too many man- made vitamins for my tastes, would rather see the vitamins come from the ingredients- not from supplements.
Potatoes, Duck, Duck Meal, Potato Protein, Canola Oil (preserved with natural mixed tocopherols), Dicalcium Phosphate, Potato Fiber, Natural Flavor, Calcium Carbonate, Sodium Chloride, Salmon Oil, Flaxseed, Potassium Chloride, Choline Chloride, Taurine, Natural Mixed Tocopherols, L-Carnitine, Yucca Schidigera Extract, Vitamin E Supplement, Iron Proteinate, Zinc Proteinate, Copper Proteinate, Ferrous Sulfate, Zinc Sulfate, Copper Sulfate, Potassium Iodide, Thiamine Mononitrate (Vitamin B-1), Manganese Proteinate, Manganous Oxide, Ascorbic Acid, Vitamin A Supplement, Biotin, Niacin, Calcium Pantothenate, Manganese Sulfate, Sodium Selenite, Pyridoxine Hydrochloride (Vitamin B-6), Vitamin B-12 Supplement, Riboflavin (Vitamin B-2), Vitamin D-3 Supplement, Folic Acid.
Now my bulldog Tidus used to get hydroxizine 2x daily if he gets any attacks or developed a hot spot- then we discovered he was allergic to poultry/chicken/turkey.
Hydroxizine is also a human allergy med. Could you ask your vet if this will work instead of the pred? Again, if it does not work, you can always go back to what does work.