JoshM. If you really have such a keen interest in keeping honeybees (and yes, they all sting), then do as other forum members have advised. Find out if you can get "desensitized".
There has been many beekeepers documented that are very allergic to bees that have kept bees.
You must determine how great your need to keep bees are and how far you are willing to go to be able to safely keep bees. You must never put yourself at a risk of a death situation, but if you really really want to be a beekeeper then do some research. Study carefully, speak to a doctor or one that can help to figure out if you are truly "allergic". That is what I would do.
Michael spoke of the allergic reaction of hives. That is an indication of a very dangerous situation as far as an allergy to a bee sting. You have not had the hives, but you have had swelling.
The swelling is a "normal" reaction to the venom, hives is a "dangerous" reaction.
So, Josh, see how really interested in beekeeping you are, then go from there. You will hear other comments from members on this forum too, but that is my two cents worth. Have a great and beautiful day on our wonderful planet, Earth. Cindi