loss of skin colour or pigment following an injury/trauma etc., is called post
inflammatory hypopigmentation. In your case the burns reached the layer of skin which produces the colour .
Normally it can take a longer period of time for your skin to regain the original colour once it completely heals. If the skin in that area was burnt deeper and not healed but has formed a scar(dead skin) the normal pigment may not return.
As you have had good improvement over most of your skin there are few methods you can try.
1.
Phototherapy using UV light at a good hospital near you. newer Targeted phototherapy machines are giving good results. They require multiple sittings.
2. medical therapy using creams and
ointments with sun exposure (tacrolimus, psoralens) which will work better once the doctor can see the exact condition.
3.
surgical treatment is a good option for you if its a small patch - grafting,
melanocyte transfer etc.where normal skin is grafted to the area to stimulate colour cells.
4. tattooing
5. temporary measures like cosmetic make up in your skin colour till you regain pigment.
Do keep in mind that it has been four months already so there are chances that the colour may not completely come back or may take a long treatment time. I hope this was helpful.