If you just lightly burnt your hand or skin such as on a stove or something else then there's no need to go to the ER for the burn.
Small burns heal on their own without medical treatment.
But if you've been severely burned and it's more than just a small burn then you should go to the ER for treatment.
Also deep burns that are above the 2nd degree mark are always an emergency such as a (3rd & 4th degree) are always an emergency and needs an ER visit.
If the burn covers a large area of the body then you need ER treatment.
1st degree burns rarely need any medical treatment but if you want to see the ER doctor it's not gonna do anything bad to get it checked out.
If you're in doubt about the severity of the burn or it seems to be getting infected then you should go to the ER just to be safe.