I did exactly the same thing some years ago and god yes it was extremely painful. However, putting my foot in a bowl of cool water removed all the pain, instantly, and also meant I had no blistering or skin damage. I had to keep the foot in the water for hours and hours, but it worked.
I just don't understand the advice about clingfilm! It was always said that with any burn you must cool it instantly with cool (not cold) still (not running) water. The mechanism behind this makes perfect sense to me, whereas the clingfilm doesn't. Maybe someone who works in medicine can tell us why that advice has changed - if it has?