Uggghhhh, I'm so tired of vets pushing Science Diet.
We have dealt with food allergies here. Ellie is evidently allergic to corn. She started scratching up a storm when she was put on Royal Canin Vet Diet. We couldn't go to Science Diet for compromised livers because that has corn too, so we started homecooking again. Ellie got one shot (after the benadryl didn't work) and she is only mildly itchy sometimes. This usually only happens now when she gets a piece of food with corn product in it.
The Wellness should be a good choice. Processed foods are so complex though so it's hard to say. Did you know that it can take up to 60 days for the body to detoxify and the new food to kick in? Your girl could be itchy for two months even on the new food (Wellness). Have you thought about cooking for her instead of going to Science Diet?