For whatever reason, I let myself touch the red spot instead of scratching it. I think that makes it easier for me, but again, I don't know whether that would generalize.
I did try it, and that is exactly what I turned out doing. I touched it softly, and sometimes pressed down on it with a finger. And it works! Better than anything I've ever tried putting on it. I don't know why I didn't know this simple trick. Of course people (my parents, for example) always say you shouldn't scratch, but no-one explained that it makes the itch go away faster, just that scratching can break the skin and maybe cause infection.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.