I went through the same mistaken analysis 10 years ago.
In fact, *all* wines contain sulfites. They are a naturally occurring product of the fermenting process.
USA doesn't require the addition of sulfites; it merely requires the labelling of all products containing more than 10 ppm of sulfites -- which is to say, all wines.
Actual severe reactions to sulfites are rare -- on the order of a dozen a year.
I, myself, find that after 3 or 4 liters of wine, the sulfites really get to me.