Microphone issues are a real pain in the neck! Your Skype has been working fine for a long time and then all of a sudden you can hear others but they can’t hear you. If your sound is working for your other Apps and it seems to be a Skype specific issue, I would start here.
Solution – Just quit Skype and sign back in. Please make sure you have your password written down somewhere before you do this.
I am not saying this is your solution, but it’s a good start to do this before calling for additional help.