Can I use polysporin (bacitracin and polymyxin) on oil burns?

First degree? It does not matter how the burn occurred, but the depth and magnitude of the burn. If it's a first degree burn, polysporin is fine. If it is a more severe second degree burn or a large area, best you see a doc for prescription medicine like silvadene, (silver sulfadiazine) which is better coverage for bacteria that are likely to complicate burn healing. Keep areas clean, but don't overdo it and cause more irritation.