Angie
This is an iCloud issue. More and more it's clear that when one has an iCloud or internet connection issue, Notes will gag. It's because every single keystroke or swipe of the pen is logged and sent through the iCloud server so that you can synchronize ("hand-off") to any of your other devices. Notes appears to be more sensitive to this than other apps that do similar things (e.g., Pages, Numbers, etc). Even a momentary stutter in your net connection will create a problem with Notes.
I'm running an iPad Pro (1st gen) with iOS 11.2.2 -- the problem is much, much better than before but it can still occur. Every time I see it happen it's because I'm having an internet glitch, whether it's just for a second or because I'm not in range of Wi-Fi, or my 4G signal is weak, etc. Usually I wait a second or two and it resolves -- annoying but not a real problem. Occasionally I have to quit Notes and go back to Home, and then go back to Notes.
So the real solution is NOT to delete the Notes app -- don't do that! The real solution is to ensure a solid internet connection so that iCloud, running in the background, can do its thing. I would suggest to Apple that a longer term solution is to provide a more robust buffering within the Notes app so that a hesitation or short delay in the network connection doesn't bring Notes to a halt.