So I recently got my Note 10.1 and when I got it, everything was working fine. However, when I was trying to watch a video, there was no sound coming from my headphones. I've already checked my headphones, and they're working fine. I did have a headphone plug charm in it for quite sometime though. Can anyone help?
Assuming you have already tried rotating the headphone jack around in the receptacle and pulling it in and out to see if you can get at least one channel working, you may have inadvertently bent or damaged the ground contact or broken part of receptacle off of the board inside.
I would suggest first trying to clean it out with an air can (compressed gas duster) or a dry qtip as Jennifer mentions above. Do not put anything moist in there. Try multiple headsets to see if anything happens.
If there is still nothing and you are feeling adventurous, you might want to try removing the backplate of the tablet to inspect the receptacle plug yourself.
Samsung Galaxy Note 10.1 Teardown - iFixit
Don't bother if you are going to send it out for repair though.
Those charms are a really bad idea. It is easy to damage a 3.5mm headset jack when there is something sticking out all the time to leverage the internal contacts with mechanical force if you bump the tablet into something and strike the charm. Usually people damage the headset receptacle when their headset is plugged in and their head moves quickly away from the device and either rips the headset off of them or the jack out of the plug at an angle.