Hello Fiona-Bain,
We'll be happy to help you in Apple Support Communities today.
If we understand, all your apps connect to the internet, no problems on Wi-Fi. But when using cellular data, the only app you can get to access the internet is YouTube.
You can select what apps can and cannot use cellular data, and it sounds like the cellular data may be disabled for these apps. Just go to Settings > Cellular and scroll down to see if Safari access needs to be enabled. Also, while you are in this setting you can go ahead and check on the other apps that you've tried to use with cellular data to see if they need to be enabled. Here is the link with details on cellular data settings: View or change cellular data settings on iPhone - Apple Support.
Reach back out to us if you still need help.
Take care!