climbed under

 If the concrete slab were near the top of a large pile of rubble, the rescuer might very well have had to climb to get to it. To me this phrasing doesn't imply stairs or a ladder, no. "Crawled under a slab" sounds to me as though the slab were very near the ground. Maybe "climbed a pile of rubble and crawled under a concrete slab" would be crystal-clear, but your sentence works for me.

 

I'd say "attended to her injuries," but "treated her injuries" is more direct and a better choice.  

 

 

 Hi New2grammar

A medic climbed under a concrete slab to reach a 5-year-old kid...  (Should be hyphenated.)

The Cambridge Dictionary defines climb as

to move into or out of a small space awkwardly or with difficulty or effort

 

Since it is not a flat surface under the slab, "crawl" may not be the appropriate word.  I think they do need to climb up and down on the rubble within the very narrow space.

I also think you need the "to" after attend in this case. 

When you crawl, you stretch out your body along the ground or you're on your hands and knees.  This normally happens on a flat or close-to-flat surface.  We say "climb on the rocks" instead of "crawl on the rocks".  The action they need in such a situation is more like climbing on rocks instead of crawling on a surface.  The inside of an air vent is a flat surface.

The muscles you use in climbing are different from that in crawling.  For example, you often need to use your fingers to grab on to something when you climb but you don't when you crawl.