What is this strange coughing sound? Is there a doctor in the house?

This will be hard to describe but I had a sinus infection around the first of Jan which is now gone. I coughed so much during that I developed a weird cough. It feels like my throat almost totally closes when I cough now and feels & sounds like the air is being forced out really hard. It feels almost like a flap at the bottom of my throat closes (right about the area where the collarbone comes to the throat in front.) when I cough and it seems like the air from a cough is trapped at the throat and is hard to exhale the cough unless I back off on the pressure behind the cough. It happens primarily when I am congested so it may have something to do still with the sinus drain? It sounds terrible, and it feels like I may exert too much pressure on it when I cough and it may damage something. Again, it is very low in my throat by collar bone, it is not in my chest or lung area. From diagrams I have looked at it seems like trachea area. What could it be?