You can try going into Recovery mode, and clearing your cache there, it may or may not help. This won't erase any important data.
To wipe the cache partition, follow these steps:
Turn off the device.
Press and hold the following three buttons at the same time:
Volume Up key
Home key
Power key
When 'GALAXY Note 3' appears on the screen, let go of the Power key but continue to press and hold the Volume Up key and the Home key.
When the Android System Recovery screen appears, release the Volume Up and Home keys.
Press the Volume Down key to highlight 'wipe cache partition.'
Press the Power key to select and wipe the cache.
With 'reboot system now' highlighted, press the Power key to restart the device.