Bad luck, lapin_rouge.
As best I understand it, the sensitivity is to sulphur dioxide gas. Sulphites added as a preservative before bottling (to prevent premature oxidisation) equilibrate in solution with the liberation of a certain amount of sulphur dioxide. Some gets bound, and some remains free.
There are certain wines marketed under the “natural” banner which eschew the addition of sulphites, though that isn’t necessarily an answer, because there is going to be a natural level of SO2 in the wine from the fermentation process. Plus, the longer term storage properties of that wine may be adversely affected. Still, it may be useful to know they exist.
Sulphites/SO2 may also be used at other times in the winemaking process prior to bottling.
I’ve a feeling that other low added sulphite level champagnes would include Marguet and Bollinger. Roederer and Drappier also use low levels of sulphite addition, and there are other growers who do this too.
Incidentally, have you been tested to confirm that this is truly the allergy you suffer from? I think it is the case that many people who regularly suffer a headache after drinking certain wines test negative for reacting to SO2, so presumably are reacting to something else. A useful test might be to see if you react to eating some dried apricots - they are usually packaged using high levels of SO2 to stop them discolouring.
Beyond undertaking chemical analysis on each line, I’m not sure there’s any way of knowing how much free SO2 is present. I don’t know if it might help, but a splashy decant before serving may help as it is a volatile gas. No promises though.