Hi Brodieg,
Welcome to Apple Support Communities! We appreciate you reaching out for help with this issue you're experiencing when receiving an incoming call. Let's get to the bottom of it together.
To start, please let us know more about what's going on. You mentioned that unless you're using your headset, your iPhone isn't ringing when you have an incoming call. Is this correct? Does your iPhone vibrate, or otherwise indicate that there's an incoming call?
Are you experiencing similar audio issues in any other apps? For example, what happens when you play a song or video? Are you able to hear all sound clear from your iPhone speaker?
Is your headset connected via the Headphone or Lightning port on your iPhone, or is it connected wirelessly via Bluetooth? If it's connected via Bluetooth, what happens if you turn off Bluetooth in Settings > Bluetooth, then place a test call to your iPhone?
Be sure that the Ring/Silent switch is set to ring. The following guide has more information:
How to put your iPhone on vibrate, ring, or silent mode - Apple Support
If it's still not ringing, head into Settings > Sounds, and verify that the slider under RINGER AND ALERTS is set loud enough to hear, then test again.
Let us know if this information helps, or if you've got any questions.