I wondered about that, too, and from some quick poking around, it does seem that you can have a delayed local reaction to latex or the processing chemicals, but anaphylaxis would be immediate. Here's a couple of summaries.

I have a mystery allergy - all I know is that three times, three to four hours after eating a certain dish at a certain restaurant, my whole body broke out in hives, and the first time I did have some upper respiratory constriction. I've never had an anaphylactic reaction to any other food, including any of the ingredients that I'm aware of in that dish. So it's possible you may never know what it was that set you off.