Your father needs to see an allergist. In the meantime, here's what my allergist helped me find.
I was nearly in the ER after eating a chicken pot pie once. It's amazing how many unnecessary ingredients are in those things. The one I ate had over 100 things!
Processed foods are the worst. It's often the additives, not the meat, although beef and pork are on my list of things I eat in small servings because they contain natural sulfite, my worst allergen/intolerance.
Itchiness and hives (red bumps) sound like a true allergy, not just my intolerance. Razzle has more knowledge than I do about allergy to sulfite.
Keeping a very good food journal will help find the meals that trigger the reaction. Then you have to do "challenge testing" to see what part of the meal is the real culprit. Please put some key words into the search box at the top of the page to find reams of descriptive posts.
For me, it's not the meat in the hamburger, it's the condiments. It's not the waffle (unless I eat too much of it), it's the maple syrup. And don't get near me with gelatin! Corn if fine, but products made from corn make me quite ill (dextrose, corn syrup, corn starch). There was probably corn starch in the pot pie, also garlic, dextrose, corn syrup, and many other known food triggers.
Let us know how he's doing.