Hello,
When touching and holding an app, it may not jiggle if you have Zoom on. I would check this in Settings > Accessibility > Tap Zoom > Disable and try again
If Zoom is disabled or it did not resolve, Go to Settings > Accessibility > Touch > 3D and Haptic Touch > turn off 3D Touch - then hold down on the app and you should see an option at the top to Rearrange Apps.
I would also try to reset the Home screen and apps to their original lay out in Settings > General > Reset.
If you have created a bunch of app folders, you may want to skip that steps as it will remove the created app folders.
Speaking of folders, will it allow you to move the apps into a folder if you create one?
- Touch and hold any app on the screen until the app icons jiggle.
- To create a folder, drag an app onto another app.
- Drag other apps into the folder.
- You can have multiple pages of apps in the folder.
- To rename the folder, tap the name field, then enter the new name.
- Tap Done (iPhone X and later) or press the Home button (other models).
To delete a folder, drag all the apps out of the folder. The folder is automatically deleted.
How to move apps and create folders on your iPhone, iPad, or iPod touch