Hello. I Had Some Tonsil Stones That I Coughed Up

Hello. I had some tonsil stones that I coughed up and then noticed a piece of my tonsil hanging off In The back of my throat. I can feel it when I breathe, swallow, cough, anything. What is this and should I be alarmed? It is very irritating and sometimes makes me panick because it feels like my throat is blocked.