hk,
I'm glad your DD is OK. I hope she's feeling OK and doesn't get anxious because this happened. It is an odd incident but I can see how it could happen (such as sneezing when you're mouth is full).
You've had such a tough time with your school. I hope you give them a piece of your mind over what happened. Does your daughter have a 504? If she does, go through the incident and point out that at every point safety procedures designed to protect her failed.
If your DD has a 504, does it stipulate that she cannot sit next to a child with her allergens. Your DD is very sensitive to egg. My DD had a reaction to unseen egg protein (left over from a cooking lesson earlier in the day before she arrived at the school) that was kind of more than a contact reaction but not quite systemic and certainly not anaphylactic. Well, after that reaction and the teacher putting DD at the time out table on days egg was on the lunch menu, we had it put in DD's 504 she was to sit with her class with a buffer between her and fellow students eating hot lunch on days when egg was on the menu. The school does not serve nut products on the lunch menu, so the kids eating hot lunch were a buffer between DD and the kids bringing lunch from home, who had no restrictions. That set up worked well for us.
DD is now in middle school and has more freedom to sit where she'd like but she tends to sit with her BFFs, one of whom has the same allergies and the other who is aware (and has wonderful parents who take care with DD's allergies).