How to prevent scarring from a burn by a hot pan on my breast in which turned from grey to red to black?

Depends in deprh: This sounds like a full thickness burn which requires immediate medical attention. Partial thickness burns (2nd & 3rd degree) with blisters must be treated with topical antibiotics (bacitracin for face - silvadene (silver sulfadiazine) for body) if not allergic in order to minimize the risk of infection which may increase the amount of tissue damage. Sulfamylon for ear eschars.

Avoid sun light: You can also use a medication called hyproquinone, it is a prescription.

Silicone sheeting: It sounds like a 3rd degree or full thickness burn. Unfortunately, it probably will scar since the entire thickness of the skin has been injured. Nevertheless, careful wound care to prevent infection is a top priority. After the wound heals, applying silicone gel sheeting (around the clock for 3-6 months) is one of the best ways to minimize the scar. If more is needed, consider scar revision.