IPhone apps won't download/update?

I'm not sure what the problem is exactly. I have called customer support 3 times now and none of them were successful. I looked up things online but even the most helpful articles were for situations slightly different from mine. Here is exactly what is happening:
whenever I try to download/update an app it says "waiting", normal. But then it is stuck loading with half progress for a while then I get a pop up message saying "unable to download/update application. 'app name' could not be downloaded at this time"

I have tried resetting the network, and the data. I have tried connecting to Wi-Fi, and restarting my phone.

the first time I called customer care, tuesday, they said it was a problem with the outreach(?) network and it would be fixed at 5pm that day.
it wasn't.
I called this morning and the woman told me the same thing.
I called about an hour ago and the man told me to do the things I tried above.nothing has worked thus far.

any suggestions?
someone told me it is probably a problem with Apple, not Sprint, because I'm able to connect to the web and send/receive messages and everything just fine. The apps are the only things giving me problems.

thanks for your help.

Added (1). Also! When the pop up box shows up, you have the option to either press "done" or "retry" retrying does not work and neither does pressing done then trying again.

There may be a low network connection or you might have exceeded the memory.