If you aren't near ground O and shelter in place with enough provisions, there are a lot of people who hopefully should survive.
A friend's Mom was leaving Hiroshima or Nagasaki, forgot which, when the big boy hit. She was burned but recovered. My friend was much later born .
Never give up. Many talk if suicide because the situation sounds hopeless. I'm not saying you would. I taught on the subject and some students are of the opinion that they might as well just go the "easy way" rather than through fall out.
The worst problem for most may be down wind of reactors. Those have a long half life and contaminate way too long to hunker down until normal.
The situation for us is different than for Japan. First, if nuclear bombs hit they will wipe our our electric grid. Since we have nuclear power plants (which Japan didn't have) that becomes very serious if they cannot keep the pumps flowing causing meltdowns.
Second we are far more dependent on electricity than Japan was. All the adults at that time were familiar with a time before electricity so the transition, even if it is short term, would not be that big a deal.
Third we are far more dependent on trucking and shipping for our big cities to survive. An EMP (nuclear blast) can destroy the electrical circuits in trucks as well as the pumps that pump gas at gas stations.
Businesses were not dependent on the telephone at that time. Using snail mail was an acceptable alternative. Of course there was no email or internet to go down.
So yes, if you survive the blast and if you avoid the radiation and the dust you will not be killed by the bomb. But the after affects will be very gruesome.