Here is one way to self test. Eat some bright apricots. If you get the same reaction from eating these as when you drink wine then you have a true sulfite allergy. These bright apricots are loaded with sulfites.
Most people associate red wines with sulfites, but white wines usually have more sulfites. If you can tolerate white wines over red then the answer is not sulfites.
Now there is not much research on Red Wine Headache. It just does not get the funding like other medical topics. So many experts are making conclusion from smaller studies.
Whatever it is, it seems to be a problem with many wine drinkers. If you find a red wine that you can tolerate then stick with the one. Because all red wines are not the same. The chemistry of red wine can change based upon its age, time the day the grapes are picked and the grape varietal.
In the video I describe this in much more detail.