If the problem isn't with an app you downloaded, fixing the issue isn't as easy as going to your iOS microphone settings. Your first step should be to remove anything you've attached to your iPhone, including cases and screen protectors. Then, look at the openings of the iPhone and clear away any debris.An iPhone has three microphones. One is on the back side near the camera, and another is on the front at the top, also near the camera. There's a bottom microphone at the base of the phone next to where you plug in your phone to charge. If there's no sound at all, though, chances are it's not a debris issue.
To further narrow down the problem, test the front and rear microphones by shooting a quick video using each of the two cameras. If both of those work, check the bottom microphone using the Voice Memos app. This at least lets you determine which of your three microphones is malfunctioning. You should then turn your device over to an Apple authorized technician so that repairs protect your manufacturer's warranty.