Thanks for reaching out to the Apple Support Communities! It sounds like you are having issues with the Notes app on your iPhone and I will be happy to help out! I recommend you check out this article with steps for How to force an app to close on your iPhone, iPad, or iPod touch and close the Notes app. Once that is done, Restart your iPhone, iPad, or iPod touch then check to see if you are still seeing the issue.
If you still see the issue, check out this article to Delete built-in Apple apps on your iOS 11 device or Apple Watch and remove the Notes app, then reinstall the app and test to see if the issue is still happening.