Generally, there is rapid change in the burn scar in first 6 months and then slow changes till 2 years. From your question it looks like the burns have just healed, so be patient your burn scar is going to show many changes in coming months. Generally, second degree burns show noticeable scarring which may turn darker with pigmentation.The scar may raise above the normal skin surface, and may turn into a hypertrophic scar. you should watch for this. I will suggest to avoid above changes, you may apply a silicone based Gel / cream like Opexa Gel (Dimeticon and Ascorbyl Tetraisopalmitate Gel) or Vaniza Gel (Polysiloxane and silicone Dioxide Gel). Also wear a pressure garment to avoid a hypertrophic scar . Get physiotherapy to avoid contracture as your scar is located on elbow. Avoid any surgical intervention for scar for first 6 months unless its absolutely indicated. I think by the end of 6 months you may not have a much noticeable scar or you will be settled with a acceptable scar at your injury site.