Hello KatsiJohn,
I understand you're not seeing all of your photos in the Messages app after updating to iOS 13.1. Also, it's telling you that all your photos will appear after it has completed indexing. Rest assured the indexing it's doing is a normal process after installing an update. One of the reasons it's doing this is so your messages are cataloged for Spotlight and Siri searches.
The amount of time it takes for Messages to finish indexing depends on how many messages and attachments you had in the Messages app to begin with. I recommend giving it some time to complete and making sure you're keeping your iPhone charged during this time. You can try restarting your device if it's been more than a couple of days and you still see the same message: Restart your iPhone, iPad, or iPod touch. Also, just so you're aware, there have been two additional updates that have been released since iOS 13.1. When you're ready to, you can update your iPhone to iOS 13.1.2 using these steps: Update your iPhone, iPad, or iPod touch.
Thanks for using Apple Support Communities.
Take care!