My understanding from my dad, who was recently tested for (and confirmed) bee venom allergy, is that there are two distinct types of reaction:
Local - redness, swelling, pain, heat, itching at or near the site. I have pretty bad local reactions - the entire area will swell up to the next big joint - ie a sting on the tip of the finger swells my entire finger, a sting on the forearm gives me two days of swelling from wrist to elbow. No matter how bad this is, if the reaction is limited by proximity to the sting, you probably aren't currently allergic, though a neck sting could still be dangerous.
Systemic - may or may not have an accompanying local reaction - shortness of breath, swelling of the neck and face (where sting is elsewhere), difficulty speaking or swallowing, unexplained cough, hives on parts of the body not stung. ANY of these symptoms within a couple of hours of a sting mean you have some degree of allergy to bee venom, and according to the allergist, that means you need to be treated because the next systemic reaction could be much worse.