isa.m9,
Hmm, you can also sync from a Windows PC with the latest version of iTunes.
However, downloading directly from the App Store should work.
Try this:
1) From the Home screen on your phone, swipe down from the middle of the screen to open the Search field
2) Type instagram, the app will probably show up.
3) Delete the Instagram app
4) Go back to the App Store, and try to download again.
Let us know if you get it going.