A purple line randomly showed up on my iPhone X and soon turned white.

You'll need to schedule an appointment at your Apple Store Genius Bar. This is a hardware failure and will require a screen replacement most likely. Since iPhone X hasn't been sold for over 2 years now, it won't be covered under warranty as your warranty expired long ago.

You're welcome. If it were me, I'd probably see if you can trade the phone in and get yourself the new iPhone 12 or iPhone 12 Pro. Lot's of improvements over the last 3 years since iPhone X was released.