Download and install the Google Classroom app for iPhone/iPad. There's also one for Android. Open the app and create a new assignment. Then tap the paper clip icon in top right corner.
Now tap the Pick photo option at the bottom of the screen. Even though it says photo, you can upload videos too. You can browse your camera roll to select the photo or video you want.
And here's a bonus for you. When you attach a file to an assignment this way, Google Classroom automatically puts the file in your Google Drive folder for that class.