Hi Davidsh1313,
Yes, you are correct, voicemail is a function of the carrier, but let's make sure your iPhone is running properly.
First, close the Phone app, and reopen it so the app refreshes with the network: Close an app on your iPhone or iPod touch - Apple Support
1. From the Home Screen, swipe up from the bottom of the screen and pause in the middle of the screen.
2. Swipe right or left to find the app that you want to close.
3. Swipe up on the app's preview to close the app.
We also recommend restarting your device and keeping it updated as those steps assure you have cleared out any minor software issues and are running the most current version.
Restart your iPhone - Apple Support
Update your iPhone or iPad - Apple Support
We hope that helps. If not, please reach out to your wireless carrier to make sure everything is provisioned correctly on your account.
Cheers!