Hello Candice,
Thank you for using Apple Support Communities. Sounds like you're experiencing issues with your Notifications. Specifically, you’re seeing them appear in rectangle animations. If so, we’d like to recommend some basic steps you can try to see if that helps out. First you want to try restarting your iPhone. This is a simple step but it does help refresh things: Restart your iPhone - Apple Support
1.) Press and hold either volume button and the side button until the power-off slider appears.
2.) Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3.) To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
Additionally, if you have any pending updates available on your device, it would be a good idea to install them. Keeping your device up-to-date can help resolve various issues and also help with performance. Just in case, the following resource can guide you through the update process: Update your iPhone or iPad - Apple Support
1.) Back up your device using iCloud or your computer.
2.) Plug your device into power and connect to the internet with Wi-Fi.
3.) Go to Settings > General, then tap Software Update.
4.) If you see more than one software update option available, choose the one that you want to install.
5.) Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
We hope these steps are helpful. Cheers.