We only use the Lenders frozen ones because of sesame. I haven't called in years but they told me those were save for our allergy set which includes sesame, d, e, p and t. There is a company that sells bagels that are sesame, d, e, p and t-free that you bake yourself at home called Bake'em Bagels. Not sure it is still in existence but we got bagels from them several times and they were delish.
You should check with them about whether or not they are still free of all those things but they were when I called them several times in the past.
I called bread companies for several years looking for a brand safe for DS. What I learned was that most all breads in the USA are baked on the same equip as breads that contain sesame. Companies described that sesame-free breads sit on pans "littered with sesame seeds" from other breads that baked on them previously. I think bread is a high risk food. I can imagine going years with no reaction and then getting a stray seed and reacting. DS ate bread for years that had a sesame warning label suddenly pop up. I called and heard how they bake their bread and that is what lead me on that 2 year quest. Even now there are not that many options when it comes to bread and we usually make our own. The Food Allergy Mama cookbook has a recipe for bagels that looks good but it also looks like a LOT of work! Maybe one day I"ll make them.
Sorry you reacted. Glad you are OK. Stinks, though.