If you (or a child) has been bitten or stung, the first line of treatment is to quickly check to see what caused the sting or bite such as a mosquito, ant, or bee; and get away from the situation to avoid further bites or stings.
Next steps include
If a stinger is lodged in the skin, remove it by pulling, brushing or scraping it out of the skin. Tweezers, credit cards, tape, and fine brushes can be used because the stingers are usually not embedded deep in the skin.
Wash the sting or bite area with mild soap and water.
If possible, without endangering anyone, capturing and/or killing the "bug" may be useful in identifying the "bug".
Reducing swelling and pain
I have used the following methods to treat myself and others, including children, with success.
Immediate treatment that may reduce swelling and pain consists of ice packs wrapped in a towel applied to the site of the bite or sting (frozen peas or corn can be used instead of ice as it will conform to the injured area).
Use acetaminophen or ibuprofen containing over-the-counter medications to reduce the pain. Avoid aspirin use in children due to the risk of Reye's syndrome.
A paste or watery mixture of baking soda applied topically may help reduce itching; calamine lotion or creams containing hydrocortisone or agents like lidocaine will also reduce itching and pain.
Over-the-counter medication containing diphenhydramine (Benadryl) can be taken orally to reduce itching.