Chiggers and mosquitoes have been really bad this year, and I seem to attract more than my fair share. I seem to be especially sensitive to them, and itch for days and days. I've tried hydrocortisone and benzocaine cream (Lanacane) with not much luck.
You can also dab mosquito bites with clear ammonia. After reading the main ingredient in a "bite stick" is ammonia, I decided to give it a try. It stopped the itch instantly. It's thrifty too!
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Kids and bugs don't always mix well. When we get bug bites, I put cooked oatmeal right on the bite marks. If the marks are really bad then I will put clear plastic wrap on top of the oatmeal, try to keep it there for 5 to 10 minutes.