I too am sensitive, but not allergic. Yet. Makes me swell more than average folks and takes longer to go away. Also, hands & feet will swell more because we want to keep using them & don’t give the swelling a chance to go down. And they’re full of nerve endings 
Listen to Dawn’s advice on the meds, and elevating your hand & using ice packs.
A couple old time remedies that do work are moistened tobacco which you can take from a cigarette, and a bit of baking soda made into a paste. They work because they’re both alkaline & help neutralize the acid of the venom - so they’re only effective in reducing pain & swelling right after you get stung.
About the stinger, Dawn is right, scrape it out asap - it’s my understanding that the venom sac remains attached to the stinger when you’ve swatted the rest of the bee away & keeps pumping venom in. Stingers are made of two serrated parts that move up and down, injecting you with more venom the longer they stay in your skin.