Sorry about your daughters allergy, I have allergies myself, not fun… however trying to equate her allergies with passing off petroleum as food is a bit of a stretch, no?
Red #3 is not food by any definition, no living creature, beyond some very specialized microbes are ever found eating petroleum. It is known to contributes to neurological issues and many other things.. it’s not food.
Extracting color from bugs shells may not sound appetizing, but bugs are things that do get and can be eaten. Petroleum is not a food.
Carmine is not made from petroleum so, no, it's not a stretch. It's the insect component.
It took us a couple years and it was done by listing everything she ate before she broke out and the looking at the ingredient lists of the products.
Mostly it was extremely dark chocolate products that was causing the problem and when I investigated how they made things like Black Forest Cake, etc, that's when the common ingredient became apparent.
Carmine is also used in some yogurts.
Insect shells have chitin in them which is the substance in shellfish such as crab, shrimp, lobster and also mollusks that triggers an allergic reaction in people with "shellfish allergies."
Depending upon the individual the reaction can range from mild to severe.