Babies, children and bee stings

Symptoms of a sting
A red swelling will appear immediately in the spot where the insect has stung and this can cause a throbbing pain and feel very tender. This will pass over the hours that follow and almost certainly present no discomfort by the next day.
If the child has been stung several times (but not just once or twice), there is a danger that the body might have taken in too much of the insect's poison ('venom'). The child might get a fever or be sick, which means that suspected intake on this scale should be checked out by a medical professional.

Treatment for stings
Home remedies include dabbing malt vinegar (the kind you put on chips!) on the wound. This immediately reduces swelling and discomfort. (This worked very well for us when our poor daughter was stung by a bee at her first birthday party. It is useful to bear in mind if you are in a park, and there might be a cafe nearby.)
Baking soda has also been recommended, rubbed lightly onto the skin around the wound.
A cold compress or ice wrapped in a flannel (so it doesn't burn the skin) can help reduce the swelling and throbbing sensation.
There are many insect bite treatments on the market but make sure you choose one which is suitable for infants, if you want to keep one in your cupboard at home.
If your child has been stung by a bee, there may still be a 'stinger' (which looks a lot like a splinter) in the wound. Remove this as quickly as you can, by scraping a blunt flat instrument like a blunt knife or your fingernail across the wound to sweep it out. If you squeeze on the stinger, the danger is that you will cause more poison to ooze out into the wound before you get it out.

Allergic reactions
If you already know your child is allergic to stings and bites, you will no doubt have a pre-prepared treatment with you at all times in case such an incident occurs.
If you do not know if your child reacts badly to stings, bear in mind the following danger signs. When stung, she may get: an itchy, blotchy and irregular raised rash; she may have breathing difficulties; the swelling may seem extreme and does not go down after a few hours; there may be swelling to other parts of the body (including the tongue); her face may swell up. If you experience any of these symptoms you should seek medical help as soon as possible.
If it possible your child has simply had a bad reaction and not an allergic one. But you should be advised on this by a doctor and act accordingly in the future. (In extreme, long-term allergy cases of this kind, treatment can be given in the form of vaccine.)

Avoidance
Teach your child that bees, wasps etc do sting and should be avoided. That they should not be taunted or played with and that they should not be trapped. Also, that you child should draw an adult's attention to the flying enemy in case it crawls into a shoe (for example) and remains there unseen.
HOWEVER, do not scare a child so that he or she is hysterical when a bee or wasp is spotted. Calm avoidance is far better and it will make the child easy to treat if they do suffer a sting.