First, go to iCloud.com and verify that all your notes are there. If they are, try restarting your phone; it may take a little while for your notes to download again. If this does not recover your notes, open Settings, tap your name, tap iCloud and turn of Notes. If prompted to keep your current notes, answer yes. Then toggle the Notes switch back on; this will force the notes to be downloaded to your phone.
Now regarding backup, in the same screen as above, scroll down to show iCloud Backup is off or on? If it's off and you are not backing up your phone on your computer, you have no backups which is a less than ideal situation. Please refer to this document that explain how to back up your devices (you need to back up your iPad as well): How to back up your iPhone, iPad, and iPod touch - Apple Support