Unless the burn is severe (heavily blistered, areas of numbness), you don't really have to put anything on it.
Keep it clean, keep it covered with a bandaid for the first few days, and apply a mild emollient cream if you want to. Silvadene (silver sulfadiazine) cream, which is often prescribed for burns, is unnecessary for small localized ones. Antibiotic ointments like neosporin & Bacitracin are also unnecessary.
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