I was thinking of neosporin only initially through the first 2-3 days after the burn, but you need to get off it so the burn will have air to dry up. I used aloe vera for a week. It seems to not hurt but it looks like it will leave an ugly scar...!!
Once your burn is completely healed. There are bleaching skin care products you can use. Glycolic acids work very well in lightening the skin tone. An exfolliant works well also. I don't know how large an area you burned but I would protect that area from the sun when outdoors with a visor, baseball hat etc. and more important wear a spf daily