I somehow deleted my notes. Is there a way to recover them?

If there is a Recently Deleted folder, it will be in Notes with the other folders.

As far as a backup, you would either have to set up iCloud backups and have the device connected to wi-fi and power overnight, or you would have to connect the device to a computer with iTunes and plug the iPhone into the computer and create a backup. Unfortunately, if you are not backing the phone up, then there is no way to recover deleted information. Also, after a data problem is not the time to find out that you should have been backing up the iPhone. This explains the two types of backups and how to set them up. About backups for iPhone, iPad, and iPod touch - Apple Support

If you go to Notes, then Folders, if there are recently deleted notes, that folder would be listed there. If not, do you seen notes under iCloud or On My iPhone? If in iCloud there still might be a way.

If you have a backup that was made when the notes were on the iPhone, you can restore to that backup. However if you have created a backup since they were deleted, you will not be able to recover them. Also, restoring to a backup brings the phone back to that date/time and anything done since then is lost. Check to see if you have a Recently Deleted folder there that you can restore notes from.