I Had A Tonsillectomy On August 10th 2015. Since August

I had a tonsillectomy on August 10th 2015. Since August 29th 2015 I have had what feels like a piece of skin in the way back of my throat. Sometimes its up really high like behind my nasal cavity and sometimes it dangles down into my throat. I can move it around with the back of my tongue and on frequent occasions it gets into a position where it makes me cough and gag uncontrollably. I went to my ENT who just looked in the back of my throat with a tongue depressor and said there was no food there and sent me home. It is now end of October and it is still there and not getting any better. I have tried gargling with warm water, salt water, netti pots, etc and nothing is getting rid of this. Please help!