Sorry for the inconvenience caused, this is not the expected behaviour from the device, but from what you've specified, the issue might be due to your full storage, so I suggest you to free up some space or use iCloud to backup your data.
If it doesn't work then use these following steps to resolve your issue:
Check if your iPhone is running on the latest version by going to the software update tab in general settings of your device.
Even if this doesn't resolve your issue, Reset all settings.
Even after this your issue does not resolve, Backup everything on your iPhone using your Mac or iCloud.
Erase your iPhone and install a the latest version again(might be software issue).
and even if this doesn't work then take your device to apple service centre as there might be hardware issue that's causing it.
Topic:
App & System Services
SubTopic:
Hardware
Tags: