I'm no expert on stings, but having had my share, I think care needs to be excersized if you are having more than a localized reaction. Swelling, and itching are normal, and it's doubtful anyone has ever died from swollen fingers or arms, or even face. However, if a sting on the arm were to result in swelling and hives on the opposite arm, torso, or legs, it is likely a systemic reaction and might be a red flag for a problem. Difficulty in breathing, shallow rapid breathing wiould signal an anaphylactic reaction, and is life threatening. Certainly not something to be minimized.
Most of us build up a resistance to the swelling, and the sting itself becomes a minor annoyance over time. Initially, I experienced disfigureing swelling and severe itching. (I was stung 4 times on the face) But I lived, and was advised to incur several stings per week to build tolerance. Dutifully, I "applied" a bee to my forearm almost daily. However, that was 40 years ago, and 30 country miles from medical help if it had been required. Probably not the best advice. Good thing I was was young and invincible! bahahahahahahahha