By saying “sleep screen” I take it you have one of the good kindles and not that fire crap. Press and hold the power button for over 10 seconds. This should force a complete reboot. Please let go when the screen goes off. If you continue to hold it down for over 25 seconds, you could trigger a device reset which is not a bad idea.
After it comes up, connect to a pc (hopefully not windows 10 anniversary update) and see how you are doing for storage space. I use a kindle voyage and that version complains when you are running low. My older kindle (keyboard or 3rd gen) just does what you describe in your question and thus I would have to plug it into pc and delete stuff, if that not fix your issues, contact [https://thekindsupport.com|amazon kindle support]