Sulfites, not sulfates. Big difference.
Yes, some tea can be sulfited. You have to read the labels. Most common brands are OK, but not all!
Some vitamins contain sulfites. Biotin for one.
The lists on the internet are helpful, but some go too far. It depends on your level of tolerance. You can calculate yours from the information www.learningtarget.com/nosulfites/
Click on the free book and then "knowing the demons."
If you get hives and throat closing you may have the "true" allergy, not the "sensitivity." My allergist calls all the reactions allergies. You are lucky to find a doctor who even knows about