I have a dry rough hard cough and my throat hurts so bad I can't swallow and its burning my mouth it feels like.

Cepacol & Dr visit. Cepacol lozenges have a numbing medication in them, which should help with the symptoms you describe. It also comes as a spray for the back of your throat (like chloraseptic) to give relief. If cough persists, then you should see a dr / urgent care visit to find cause.