OFF seems to repel them adequately for me, but for relief once its too late to pull up the drawbridge, I've found (don't laugh) hemp oil provides me great relief from all sorts of skin irritations. Not CBD oil. I mean hemp seed oil like you get at the grocery store. It smells a little like dried grass which doesn't bother me but if the odor annoys you, a few drops of lemongrass essential oil or something similar covers the odor up. Just rub it on, it is absorbed by the skin fairly easily, one of the few oils that does that. The other I know of is camellia seed oil (from tea plants) and that is quite expensive in the US. It's also good for your hair but that is another kettle of fish.
I'm not into "alternative" medicine (and I'm not all that into medicine altogether) but for years I've had contact dermatitis of "unknown origins" (recently discovered to be allergies to anything palm related, eg the various coconut derivatives that are in EVERYTHING from soap to paper towels these days). It was "treated" with a permascription for cortisol cream, which I ran out of one day. In desperation I rubbed some hemp oil on the rash, because I had some on hand and not terribly reliable sources on the internet said it was good for this purpose. Like I said, desperation.
Much to my shock it worked. The relief was immediate. In fact it worked better than the cortisol cream I'd been using for years. Possibly just by relieving the itching so it didn't get scratched but hey, I'll take it as a win.
It takes a little longer for things like mosquito bites. I got swarmed by ants at one point a couple years ago and it relieved that almost immediately just like the rash from my allergies. I bet it would help relieve the suffering of chigger bites as well. Possibly worth a try if you're in that unfortunate situation.
Due to my now identified allergies, the only things I put on my skin any more are hemp oil and bag balm. Bag balm is the only commercially available product (that doesn't require me giving up my firstborn grandson) that contains absolutely no palm-derived substances. And yes, I make my own shampoos and use only 100% pure olive oil soap (or bittim which is pistachio oil derived). And if something bites or stings me, bug-wise, the hemp oil is ready at hand. I buy a big bottle of hemp oil, freeze most of it so it doesn't go off (hemp oil is fairly short-lived), and keep a small amount in a dropper bottle.