All wine has sulfites. Many people attribute an allergic reaction to red wines by blaming it on sulfites. Most people are not allergic to sulfites. The truth is that there are more sulfites in raisins, milk and other various foods that we consume daily, as well as in the air itself.
Sulfites are a preservative and a natural occurrence in winemaking. If the wine has no sulfites, or if you remove the sulfites from wine it will very rapidly turn to vinegar.
While sulfur dioxide has primarily been used to prevent oxidation in wine, new research is showing that it does much more. Adding sulfur at various stages of winemaking broadly affects a wine's chemistry, from its aromatic compounds to its texture.
So please enjoy the red wines and be aware that most likely you are having a reaction to something more complex than sulfites. Such as the new oak barrels or the minerals that are in the soils. Or even perhaps the chemicals some vineyards are using as pesticides. Please drink responsibly.