Ever since I started beekeeping I've run into so many people who tell me, "I'm allergic to bees." When asked about symptoms, they say, "I swell up."
Well, pretty much everyone swells up to one degree or another when stung. The dangerous reaction is anaphylactic, when breathing becomes difficult and emergency care is required. Some beekeepers carry epinephrine kits so they can inject themselves just in case.
I've been stung under my eye with no reaction, and stung on my eyelid with a tremendous reaction. I've been stung on the hand and had it swell up like a catcher's mitt, and stung on the stomach with little more than a pimple resulting. So, it varies. But swelling doesn't mean you're allergic, just means you're normal.
Here's a handsome photo of me within about an hour of getting stung on my right eyelid. Anyone wanna make out?
For more info on anaphylactic shock: http://www.webmd.com/allergies/severe-allergic-reaction-anaphylactic-shock