This is very painful and I’m not sure what to do about it. It started as a small burn spot (cooking injury) in the nail and has since expanded to this.
That must have been quite a deep burn and it certainly looks painful. You may have an infection in there so do see your doctor.
As Marina said, the burn seems to have been much deeper than it appeared to you at the time of the accident. You should definitely see a dermatologist because deep burns leave the deeper layer of the skin exposed to various types of infection. I hope you get better soon!