iphone 6 plus suddenly won't update or download apps

My iPhone 6 plus recently stopped updating/downloading apps. It's a 128gb memory, and I'm only using half of that. I've backed the phone up on my computer. It's running the latest operating system. Last night, my husband called TMobile and they had him Reset Network Settings. About half of the apps in the queue updated at that point. Tried to do the same Reset this morning but it hasn't helped this time. Tmobile connected us with an Apple Care person, who had me do yet another soft and hard reset. I've deleted all apps that were currently trying to update (and a couple others). Now it won't download them back to the phone either. I've logged out and back into my iTunes apple account.

What now??