I would absolutely not give her any more of the product. It does sound like an allergic reaction, and if it is, the next dose will be even worse. It sounds in fact like it may be an allergy to something she's already ingesting - try a simpler food (fewer ingredients) . I just looked at the ingredient list for Science Diet Indoor Dry - just one picked among all they have. It starts with
"Chicken, Whole Grain Wheat, Corn Gluten Meal, Animal Fat (preserved with mixed tocopherols and citric acid), Powdered Cellulose, Pea Bran Meal, "

Cats do not need grain like wheat or corn - and these are the second and third ingredients in the list!

I'd transition her to a simpler food, maybe a grain-free one, even a wet food and see if that helps her skin. Do not use any more of that product on her until you try the new food for a few weeks, okay? In fact, keep the receipt, you may be able to get a refund if it turns out you don;t need it!

Good luck, and let us know how it goes! And bless you for not waiting until there are actually bald spots, for catching this early!