Here are a couple of suggestions, some may work for some, and not others. We heard from someone that you could use a hair dryer. We turn it on high, and aim it at the bite. We keep it the same distance away as you would when you dry your hair. We keep it there til it hurts too much, and then we go on to the next one. It works great for my husband. Something else that he does for his bites, chigger, ants or whatever, is to get his adrenaline going, and get sweating. He usually gets the bites when he is working outside, and he is working hard mowing, or whatever, and they go away really fast, sometimes by the next day they are gone. If he gets a bite after he is done, he has to use something else on it, such as a hair dryer.
Something I read that is a good mosquito repellant, so should work for all insects I would think, is vanilla extract. My husband used to play golf at a course that would keep a spray bottle for the guests to use, and he said it worked great!
Carrie