How long does the redness from a burn last? Its been two months!?

I got a 2nd degree burn two months ago. My car radiator cap blew off buring my arm severly. I went to the ER and they scd the loose skin off to prevent infection. I was given a silver sulfadine cream that was wonderfully healing. I stopped using it after 10 days and no longer needed a bandage. I do not appear to have any scars but my skin is still a discolored red after 2 months! how long does it take?