Just bought iPhone 8 Plus with 20 month contract

Ok, you can't 'upgrade' your iPhone unless you're on the iPhone upgrade program.

Here's some information on the iPhone Upgrade Program: iPhone Upgrade Program - Apple

How to Join - iPhone Upgrade Program - Apple

Here's information on AppleCare: AppleCare - Apple

The following link has information, including the excerpt below. AppleCare+ - iPhone - Apple

Purchase AppleCare+ with your new iPhone. Or buy it within 60 days of your iPhone purchase:

• Online (requires you to verify your serial number and run a remote diagnostic)
• At an Apple Store (inspection of iPhone and proof of purchase are required)
• Or call (800) 275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

See AppleCare+ Terms and Conditions for complete product details.