I have had this concern become an actually issue with the monkey!
Basically you just do the same thing you would do for you for your pet --- dog, cat, monkey ..
Of removing the stinger if it is still in them, and NOT pinch it out, the best way is scrape it out like with a credit card ...
then watch them for breathing changes, do KNOW that often they will have a faster heart rate than normal, just as you would from the surprise and ouch of it (this terrified me with the monkey because hers was fast a LONG time) odds are you will NOT have an allergy issue, however it can happen, and you treat with antihistamines just like in people .. i do KNOW you can use a kids liquid kind, shoot it in the mouth BUT am not comfortable with the HOW MUCH.. per weight per animal
however if an animal has an allergy it is more likely to be a swollen ouchy place then a breathing issue and for that you treat again like you would you .. there are antihistamine salves you can rub in to it, and or make a poultice of ash and water or baking soda and water ..
regardless of choice you do not want a lot that the animal is licking off and taking IN ..
usually they are like kids, way tougher then we think, and not even phased