After a bee or wasp sting, you will notice a small, itchy bump, which rapidly disappears. This local reaction is caused by the insect’s venom, not an allergy.
For certain sensitive people, a local reaction which is also allergic and can be much more serious: a painful red swelling which may spread and last a couple of days.
Stings can also provoke generalised reactions with a variety of consequences (urticaria, oedema, vomiting, diarrhoea, rhinitis symptoms, an asthma attack, anaphylactic shock).
Just because you had a bad, generalised reaction to one insect sting does not mean you will necessarily react the same way again, although there is a 50-50 chance you will.