No. Airburst nuclear bombs for the most part don't make things radioactive, air pretty much can't become radioactive (pure water also can't become radioactive, although you can mix radioactive elements into it of course).
Ground blasts are worse, but it's the ground itself that becomes radioactive, not the things that are far away and are affected by the blast.
And no one purposely does ground bursts, because they don't do a good job of damaging things with a blast - most of the energy ends up reflected into space, or absorbed into the ground. (I guess a terrorist might want to, since they don't have military strategic goals.)
The material of the bomb itself is radioactive of course, but there isn't usually all that much of it, and it's dispersed quite widely.
Her journals did not become radioactive because they were neutron-activated, but because they were contaminated by radioactive material. But there's a limited amount of that, so only a small amount of material becomes radioactive that way.
(Note: I'm speaking relatively here, if you have a sensitive enough detector you'll find stuff of course. That's one of the things that makes people so scared of radiation - it's so easy to detect at even minuscule levels, while far more dangerous things are harder to detect so no one reports them.)
Water can and does become radioactive through neutron capture breeding tritium.
However, neutron flux falls off quickly with range, and for an airburst explosion it would not have been high enough at the surface to cause significant neutron "activation" of local materials. Almost all of the fallout from the blast came from the material in the bomb itself.
That's true, but atom bombs make very very little tritium.
To make tritium you need to start with deuterium, which is already rarely made by atom bombs. So you have two rare events that have to happen in sequence.
So that means that atom bombs pretty much don't make any.
Little Boy was air burst 580m above the city, so most of the fallout traveled away into the atmosphere.
There were many acute radiation poisoning deaths (though there were far more deaths from the fire and the blast), and about a third of the survivors suffered radiation injuries that increased their risk of cancer, but there was very little to no long-term contamination of the area.
