Exactly this, I get regular blood work. On top of that, I can feel the inflammation. It is pressure, or warmth. It's a very obvious bodily reaction. Now of course for the average immune system the effects would be more subtle, but could still be noticed in energy levels, focus/attention, etc. And even if not noticeable, low-grade inflammation long term is one of the main factors of age-related decline.

As for attributing a body's reaction to a single food, there's something called the elimination diet where one isolates the variables one at a time. https://en.wikipedia.org/wiki/Elimination_diet?wprov=sfla1