What if the update isn’t showing up and my phone says it’s updated with the lastest?

Not all iPhone can update to iOS 13, it depends which iPhone model you have.

Settings > General > About > Model > ?

iPhone 6 and 6 Plus cannot update past iOS 12.4.2.

It is not eligible for iOS 13.

Apple has released an iOS 12.4.3 on the 28th Oct, 2019 for iPhone 5s, 6 and 6 Plus.