That is at least a 2nd degree burn even if its not all up and down your arm can be VERY painful. 3rd degree would be tissue death from the under layers of skin. PLEASE go to the ER. you are risking a serious infection from this. Burns are NOT to be played with. Even if you feel silly GO! The fluid shift that happens in burns causes your electorlytes to go whacky and can throw you into some trouble. PLEASE go to the ER.

By the way, a damanged nervous system can confuse pain for itching. What you are feeling could be nerve pain from damage nerve tissue from the burn. it means its on the edge of a 3rd degree burn and you need help. please go.