Allergic Reaction to New Dry Food??

Hi all,
I am new and concerned about my cat, Luna.
Last month I slowly tried to change my 10month Luna's dry food to something better. Her normal food is Purina One and the new food I gave was small abouts of Taste of the Wild dry. After about a week she started throwing up several times a day, was letharic, seemed to breathe louder through her nose, and stopped eating.
I took her to the vet and got a blood test. Luna had a very high white blood cell count but everything else looked normal. Vet couldnt pinpoint the reason for Luna being sick but was concerned about the new food I gave her. Several nights at the vet and giving her medicine made her better.
I kept her on her normal dry and wet food for 2 weeks after she got better, and she was fine and her normal self.

Just this past weekend I decided to try her on another new dry food; Chicken Soup for the Soul dry cat food. I gave Luna less than half of it mixed in with her normal food on Saturday and mixed in even less on Sunday. Today (Monday this morning) she showed the same sickness symptoms. Vomited, lethargic, slightly noisier breathing. Except this time she seems to also be drooling a little.
Could these symptoms be an allergic reaction?
So far the only similarities I see that the 2 dry foods have is that both are manufactured by Diamond and both have peas and potatoes in the ingredients.
I plan on taking her to a different vet if the symptoms dont go away. But this is driving me crazy.

Thank you for any help and sorry if this is in the wrong section.

Welcome to The Cat Site, and I'm sorry Luna isn't feeling well.
Based on what you write, it seems as though Luna may in fact have an allergy to peas and possibly potato, though the nosier breathing is a bit odd. She also might be allergic to the protein, fish or venison, for example.
Both products have a lot of ingredients in them; she could be allergic, for example, to tomatoes or blueberries.
Will Luna eat wet food? There are many reasons wet food is better than dry; for one, there are generally less additives in wet food and you can get a grain free food. Do read the ingredients carefully; grain free doesn't mean carbohydrate free. Peas and potatoes are of course carbohydrates. Some brands also have single source protein.
Keep us posted.