macbook air june 2013 - no sound - in System Pref- sound - output , only Headphones in field......

Sounds like maybe the micro switch inside of the headphone port is stuck and the sound preference thinks that something is still plugged in.

Try plugging a headphone jack in and out a couple of times to see if it will un-stick and switch the sound back to the internal speakers.

If not, then you should take it into your local Apple Service Provider and have it looked at.

Your welcome!