Hi Arthur itis, no definitley not a delayed reaction to the bee. I am allergic to wasps but not bees or i wouldn't be a bee keeper. That sting me on my chest and the swelling was my knee downwards. Also the venom from the wasp is the opposite to a bee, bee is acid and wasp is alkali I think, and the venoms react in different ways.
To take a bee sting out all you need to do is put your nail under the stinger and flick it out. Never try to squeeze it. A bee stinger has two sections which work against each other and are barbed so will work downwards into the skin whereas a wasp does not leave it's sting behind and neither, actually, does the bumble bee.