A family of Microsoft products that enable users to capture, organize, and reuse notes electronically.
An answer to your question depends on the history of your Onenote desktop installations.
Historically (in older versions of Onenote) the Quick Notes started as Unfiled Notes and were stored locally on your computer. Upgrade installations didn't change that, for compatibility.
Then came the mobile Onenotes (and the UWP App from the Windows Store). They all create Quick Notes solely on Onedrive. If necessary they create a new "personal" notebook with changing names from version to version but always with a section named Quick Notes.
So there is some probability you have two places with Quick Notes.
How to find them:
Where Onenote 2016 stores them you can see in File, O ptions, Save & Backup:
If they are stored locally then you have to modify this pointer to the Quick Notes on Onedrive.
But how to find them on Onedrive ....
Open your browser and login to https://onedrive.live.com
If you have used a mobile client or the UWP App you should find a "personal" notebook within the folder Documents. Click it to open it in Onenote Online to see whether there is a Quick Notes section. When you have found it then click Edit in Onenote. The notebook should open in Onenote 2016.
Now you have both Quick Notes sections open in Onenote.
Then copy/move all your notes from the local Quick Notes to the Quick Notes on Onedrive.
The last step is to modify the Quick Notes pointer in Options (see above) to point to the Quick Notes on Onedrive.
If all is well, you can delete the old local Quick Notes section with Windows explorer.
Bernd