How long will it take for a burn on my pinky to heal from a hot pan?

It varies: Depends upon size and depth of burn. Less deep burns can heal in a few days. Larger deeper burns can take longer. If injury is arounentire finger, should see a hand surgeon.

SImple means: 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. Ice worsens already injured skin. Cool water soaks help as can taking anti-inflammation medicines like motrin/advil. Avoid further damage as this can cause scarring .Skin cream applied daily/gently helps or protective dressings.