Hello,
Most superficial burns heal within about two weeks and don't usually leave a scarf. For these kind of burns; you can apply antibiotic cream such as silver sulfadiazine (Silvadene).It will prevent infection and help in fast healing.
One medicine which has been advised by many dermatologists for scar diminishing is contractubex gel/cream. You can seek your dermatologist/surgeon’s opinion before using this cream.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
The darker your skin the more likely it will scar.
I am fair skinned and I burned my neck a couple of times. It took a year at least for the scar to fade away for me. Put aloe vera on the burn.