Yes you do, it's your “voice box”. Might not be as prominent on some people, but it's there. Do the “C” thing and grasp the front of your neck midway between bottom & top & gently move that back & forth- that's your Adam's apple. If you're still not convinced, say “A-a-ahh” in a low pitch while you've got that in your grasp & you can feel the vibration.
A friend showed me an easy way to get rid of my hiccups. I take my thumb and index figure so they form a " C ". I take the open part of the C and lightly squeeze on each side of my Adam's apple with those two fingertips and that has always worked for me to get rid of the hiccups! It is convenient because I can do it anywhere and don't need anything other than my hand! Art