Hi, welcome to the board.
Yes, I would switch her to a sensitive and Limited Ingredient Diet. Natural Balance makes some of these. You could also look at simple ingredient freeze dried diets. Also, look into giving Sophie a good probiotic daily with her meals - to balance the good flora in her stomach and intestines.
I agree, although these kibble are "vet approved", not ALL vets approve of them, as they have bad ingredients in them.Please don’t recommend Hills or Royal Canin
All the best with Sophie!