I'm using iPhone 6s 16 GB. My storage isn't full but still I can't download anything. Every time I wanted to start a download it keeps telling:
app name* could not be download at this time
You could try restarting your iPhone and see if it solves your issue.
See my answer in this post
Usually this fixes itself server side in a day or three, but a way to triage this and ensure the device itself isn’t a problem is as follows.
At that point you should know you have free space, the delete works and more space is returned.
Then power down the device a second time. When it restarts, confirm space is correct and then re-enable the networking.
At that point, you would either wait out the update error, find a new network entirely to check if the network were blocking updates, try restoring the device entirely after making a backup and/or ask Apple Store support to check your account.