Can a bee sting cause a reaction like symptoms that of allergies from pollen like watery eyes or stuffy nose?

My step son was stung by a bee early this after noon and the site where he was stung is swollen but other then that he was fine. Twelve Hours later he is complaining that his nose is all stuffed up. My wife said that having an allergic reaction to a bee sting is the same as if he just had regular allergies like from animal dander, or pollen. Basically saying that allergies are allergies. I disagree and from what i have read the symptoms would be different then that of your everyday allergies and if there where going to be an allergic reaction to a bee sting if after 5 hours from being stung there wasn't a reaction, likely there wouldn't be an allergic reaction. i just want to see if someone could clear this up. lol