I had exactly the same problem with my iPhone. I tried everything—an air compressor, the "Change with Buttons" setting, cotton bud cleaning, dropping it on a carpeted floor—and nothing worked. Basically, my side buttons are broken. One way around this is to go to Settings, General, Accessibility, AssistiveTouch, and turn AssistiveTouch on. This brings a little white dot onto the main screen, which can be used to change various settings. Tap on the white dot, then go to Device and make sure the Mute/Unmute toggle says "Mute" (as in, you have to press it to mute the phone). If it says "Unmute," that means your phone is muted. You can also adjust the volume settings from here. I hope this helps someone!