To me, this is still sounding like a "hives" reaction in a human. Wherein the human ingested something that caused a severe reaction. In Bella's case, I'm still leaning toward that Marinade and/or the grilling (grilling, in and of itself, adds chemicals) as causing the severe reaction. It still wouldn't hurt to have a skin scraping.
Ongoing itching could really just be seasonal. Getting her onto raw, if her tummy/poo is fine, might be really good timing right now.