Does Apple Care cover a glitching iPhone?

Hi cjmccarthy21,

Welcome to the Apple Community, where some of us do our best to help each other.

Apple Support can help:

Find out if your device is eligible for Apple Care:

https://checkcoverage.apple.com/au/en/;jsessionid=node01ros0ixhgi3yctfctffpup6lt372963.node0

There is a discussion thread, where someone on iPad had a similar screen hardware fault,

seems quite similar to your iPhone:

https://discussions.apple.com/thread/252852247

If you want to try a "restart" and /or "force restart" on iPhone:

Restart your iPhone:

https://support.apple.com/en-us/HT201559

Force restart iPhone:

https://support.apple.com/en-au/guide/iphone/iph8903c3ee6/ios

Hope this is helpful to you :)