If the phone was backing up its photos to the cloud via your Google Account, you should find them at photos.google.com and they should be downloadable to a new device as well as accessible via computer. Messages are a different story. Unless they were backed up by an app like SMS Backup & Restore or something similar, they are most likely lost.
I’m sorry not to have more positive news for you.
You’re very welcome.
The Nexus is quite old now as smartphones go. It may be difficult to locate a shop that repairs them.
Lilybell2Hello Diana KM,
Welcome to the Google Fi Community forum.
You can try uBreakiFix, if you have one nearby.