Question: do you hear anything from the phone's speaker when playing music or talking with someone on your S3? When did it start happening? What did you do differently the day before or the day it happened? Did you install a new app before it happened? Can you take a screenshot of your home screen by quickly hitting the power button and the home button at the same time and then post it on this thread? That way, we can see exactly what the icon is. Please take no offense, I'm not saying you have trouble distinguish a headphone jack to something else. I need 100% proof haha
I'm not a phone expert. If I can recall, goupon may be pretty good when dealing with headphones, but i'll give it a shot.
A friend's Galaxy S2 had the headphone icon problem, so he asked me for help. Luckily, I was able to fix it. I used a toothpick, small piece of cotton, and rubbing alcohol. First, I turned off the phone and took out the battery. Then, I placed the cotton at the end of the toothpick and soaked a little bit of alcohol where the cotton was. Obviously, the next step is to carefully clean the headphone jack with the cottoned toothpick. I know it's difficult to fuck it up with a wooden toothpick, but I was still gentle when cleaning it to prevent damage to the headphone. Lastly, I put the battery back in and turn on his phone. And bam! The icon was gone!
Now, his issue is a "physical" issue where the hardware was somewhat damaged or dirty. If the icon is still there, then you may have a software issue. In this case, try doing a soft reset by turn off your phone and then turning it back on by holding the power button and volume down button at the same time for like 10+ seconds. If this doesn't work, then do a hard reset, which is resetting your phone to its factory settings.
If all else falls, then I recommend you pick up your phone with your dominate hand and throw it against a concrete wall as hard as you can. I guarantee you that the icon will not show up anymore.