In writing the following, I am excluding locations where mosquitoes are in huge visible clouds, but, in general, I find that when I move to an area with mosquitoes that initially they are a problem. I get bitten and I itch a lot.
After a couple of weeks, I don't notice them and don't seem to get bitten very much. Also, one does not notice the local folks having great problems with them.
I used to be a big buyer of various creams and potions to reduce the itchy and bumps from bites until I found the best treatment. The main ingredient is also a common material in the various after-bite treatments.
I buy a bottle of household ammonia. Use cotton wool or tissue paper. Moisten the material with the ammonia and rub it into the bite. The ammonia, apparently, has the effect of neutralizing the protein injected by bitey things and removing the itch and bump. This works best if applied just after being bitten because the ammonia can enter the bite before it closes up. You get a brief stinging sensation and a few minutes later - bite is gone. If applied later, it seems to work best after a good scratching session because the skin has been broken slightly by your scratching. It does work without scratching but is not so fast and needs more sessions with the ammonia.
You can make your own version of the pen-type afterbite treatments using alcohol-based hand sanitizer. Open up the sanitizer bottle and ditch about 1/3 to 1/2 the content. Refill the container with neat household ammonia, the job's done. Now you have a less messy, slightly less stinky, afterbite treatment that also sanitizes the bite. The alcohol has a nice cooling effect and the cost is minimal. Sanitizer costs €1 or less and the ammonia is about nothing per liter. Price of a pen-type afterbite treatment is usually in excess of €10.