I have a burn on my arm from cooking and i used aloe vera on it. it scabbed very fast but it turned black and i am concerned if it is infected or not.?

It doesn't appear so: It is the appearance of the skin around the scab that will indicate the presence of infection. Generally an infection will be associated with red skin that is tender to touch around the scab or the scab will be tender. Bleeding into a blister can result in a black scab. Intense pain is characteristic of burns initially but pain that develops a few days later is suspicious for infection.

Simple Care: Burns are the response of the tissues to injury from heat. It is simply inflammation which means increase blood flow to the area to promote healing. Depth determines care. Do not use ice worsens already injured skin. Cool water soaks help as can taking anti-inflammation medicines like Motrin or advil (ibuprofen). Avoid any further damage as this can cause scarring . Good skin cream applied daily/gently helps.