hmm...if you don't have stretchy shirts, I think for one that was too wide you could buy some elastic and gather the shirt just under the bust to give it a more flattering shape.
As for shirts that are too short, perhaps someone who has more sewing knowledge could help us, but you might still be able to use a stretchy fabric for the middle section if the rest of your shirt was non-stretchy material as long as you can stretch the midsection enough while you sew to make the whole thing stretchy enough to fit over your head. Or, if you used shirts with buttons, you could resize the midsection to be tighter, and match up the buttons in the front so they are still functional. Hope that makes some sense!
Doodleabby: I didn't even think how this could work for someone who is outgrowing their clothes, great idea! (I was just working with the ugly shirts I already own)