I am confused as to what the climax of the story is ... is it the bombing of the church, or is that the rising action?
Yes - I believe the climax is the bombing of the church and Kenny's experience of wandering inside, seeing the dead bodies, and grabbing the shoe that he fears belong to his sister. At this point, he believes the "Wool Pooh" got her - and unlike Byron was able to do for him at Collier's Landing, he is not able to save her. He carries guilt about this later. In the meantime, though, he wanders back to his grandmother's house, and the falling action begins.
In the falling action, his sister Joey returns to the house, wearing both of her shoes, and he sees that she is still alive. She tells him that he had summoned her away from the church, and she had then chased him down the street while he was wearing different clothes, but that he ran away. This adds a mysterious, supernatural element to the story since both Kenny and the reader know this is not true - prior to entering the church, he had been at the house feeling sick and depressed.
He leaves to tell his parents Joey is safe, and the whole family quickly leaves Birmingham, trying to keep the news from Joey of just how close she was to death. However, back at home, Kenny does not quickly recover from his experience. He is afflicted with a kind of post-traumatic shock disorder, and all he wants to do is hide behind the chair at the "Watson Pet Hospital" where the sick pets used to go to die.
Showing how much he has matured throughout the story, it is Byron in the resolution who finally helps Kenny to come out from behind the chair and find a zest for life again. Byron recognizes the pain Kenny has experienced and acknowledges that terrible things happen in the world, but he urges him not to give up - "that's the way it is and keep on steppin'" - and tells him it is time to "cut this mess out." He also points out that somehow, Kenny's presence helped to lead Joey from the church, so he shouldn't feel guilty about what happened. And Kenny listens - having matured a lot of the course of the novel as well; he loses much of his innocence but gains a much stronger relationship with his brother in the process.