What I have read suggests that local reactions are not predictive of a systemic reaction.
Having spent too many hours around bee hives as a child, I had no reaction at all, other than the pain, which is minor.
After taking up beekeeping as an adult (45 years later) I had no reaction for about 6 months. Then got swelling so bad when stung on a finger - my entire hand swelled up, and the finger was so swollen all the skin peeled off.
After that had less severe reactions, until now (some years later) I rarely have more than a small local reaction - a welt half the diameter of a dime.
Agree with Michael (as usual) local reactions are something to endure, but systemic reactions -itchy red hives, swollen tongue or throat, difficulty breathing, abdominal pain, nausea or vomiting, dizziness, weak rapid pulse, etc. are a medical emergency - you can die pretty quickly.
Please note, this is not a medical opinion, just me repeating what I have read in the past.