Your girlfriend sounds correct. It may sound silly at first, but the doctrine of Transubstantiation is a well developed, detailed explanation of what happens during the consecration of the bread and wine. It is not a minor thing.
The Catholic doctrine of Transubstantiation teaches that the substance of the bread, what the bread really is, becomes the Body of Christ. The accidents of the bread, the characteristics like color, taste, etc, are not changed. These are properties that are not essential to what bread is. Red bread would still be bread. The accidents include everything that you could determine using chemistry.
The human body will still react to the host because the chemical accident/characteristic of gluten(ness) (not sure what word to use there) because it remains present.
To answer a comment:
Note that the words essence , substance , and accidents have a specific philosophical meaning with a history and development that stretches back thousands of years. They don't necessarily agree with how we use the words today, especially if one is coming from a modern, rationalist-materialist worldview.
It is tempting to say that the chemistry of the is the essence of the bread, but that does not coincide with how the Catholic Church uses the term essence. An overview of that would be a good question to post (if it has not already been asked).