The length of time it takes for a burn to heal depends on how severe the burn is.
For less severe burns the burn should heal within 2 to 4 weeks and it should scab over and the burn should feel better.
For more severe burns it may take a few months or even 6 months or so for the burn to fully heal and if it's a really severe burn it requires medical treatment for it to heal.
Some more severe burns can cause infection so you need a really severe burn to be treated by the doctor or hospital.
I've had small burns take a few weeks to start healing and then after 4 weeks the burn was healed up and no longer painful.
I remember when I was living with my parents as a 13 year old and we had a wood burning stove and I backed up against it while in my shorts and burnt the skin on my leg where my legs bent behind the kneecap.
That was painful and I could hardly walk for at least a month but after a month it stopped hurting and healed up.