I stumbled across the same story just now on Facebook, and after having my feels crushed, I quickly searched and found that it's apparently "What Would Spider-Man Do?", an eight-page story from Amazing Spider-Man Vol 1 #700.5. I don't know why ".5", but #700 is the issue in which
Peter Parker dies, and Otto Octavius becomes the Superior Spider-Man.
The comic opens with Spider-Man rushing the kid to hospital after he was shot in the back.
That night, Peter confides to Mary-Jane that the kid was shot while trying to save Spidey from some bank robbers, and that he feels responsible for allowing the kid to get in harm's way.
I won't post the rest of the comic here: I feel like this is enough for you to identify that it's the right one, and the rest can easily be found on Google (it's in the first page of results for "What Would Spider-Man Do?". Warning, though: you were right. This story has all the feels.