Being owned by the world's most allergic cat, I've sort of become an expert on food allergies. Protein allergies are to a specific protein source such as fish, beef, poultry, etc. Z/D has hydrolized chicken liver and chicken. The process changes the molecular structure of the protein so the immune system is fooled into thinking this protein is not on the allergic to list.
Z/D dry had a formulation change a while back. Originally it was all chicken liver. Chicken meat was added. Protein content was reduced. and note, the sodium content is very high. Ms. Allergy, who could eat the old Z/D, had an award winning allergic reaction to the new version. Eliminating it completely showed that she never tolerated the old version that well either. All Hill's products have a lot of extras which doesn't help and they keep changing them too. European dry Z/D is different from the US and she can eat it. We have never had canned Z/D.
In fact, my other two cats reacted to the new version of Z/D too with lots of shedding and in one, dander too. The latter doesn't shed at all.
Cats, like people and just about every other mammal can be allergic to anything, veggies, supplements (that's the manufacturer), artificial color, artificial flavor, artificial scent (Fancy Feast has the last 3), thickeners, you name it. Most common cat food allergies are beef, fish, corn, & wheat. Ms Allergy is allergic to all poultry, sweet potatoes, canned pumpkin, seaweed, tomatoes, and Solgar pysillum among other things. Another of my cats is allergic to anything that says Royal Canin (yeast overgrowth in the ears).
The preferred food at my place is IAMS Veterinary Formula Skin & Coat Response LB, probably the least known of the allergy foods. Being in Israel, where supply is iffy and it has another name, raw too. When my angel HCM cat was first diagnosed, I wrote to UK IAMS about the sodium content and in a very long, technical email, they said it was okay. Z/D caused fluid retention.
Myocarditis was what killed my angel. Cause never determined as just about anything can cause it. Not only food (I will always blame Royal Canin as I was experimenting with some of their sensitive foods), fungal, bacterial, and virus infections can cause it.
So the easiest thing to do is change the food and personally, I'd look for something other than Z/D or Fancy Feast (too many additives). Okay, so Hill's canned foods turns Ms Allergy's white coat yellowish and my other cats end up with greasy fur. I'm a bit prejudiced.