How do I treat a burn from a motorcycle exhaust pipe?

I got a burn on the inside of my ankle about 3 inches in diameter. This happened about 6 days ago. At first, it was just black and blue like a bruise, it didn't hurt at all. Then the next day it started to blister and all the skin peeled off and then it hurt a lot. I have been putting neosporin on it and keeping it covered with a large bandage, changing it at least once a day. I haven't been using soap or anything on it, except when in the shower I keep the bandage off so it gets cleaned that way. The center is all red and looks bloody, with little red spots all over. The outer edge is all purple/pink. It still burns and throbs now if I put pressure on my foot or try flex my foot which stretches the skin. Is this a 3rd or 2nd degree burn? Does this sound like it is infected? Should I be treating it another way? Do I need to go to the doctor?? Any advice would be great! Thanks...

-Remove clothing from the burned area immediately.-Run cool (not cold) water over the burned area (if water isn't available, any cold, drinkable fluid can be used) or hold a clean, cold compress on the burn for approximately 3 to 5 minutes (do not use ice, as it may cause the burn to take longer to heal).-Do not apply butter, grease, powder, or any other remedies to the burn, as these increase the risk of infection.-If the burned area is small, loosely cover it with a sterile gauze pad or bandage.-Give acetaminophen or ibuprofen for pain.-If the area affected is small (the size of a quarter or smaller), keep the area clean and continue to use cool compresses and a loose dressing over the next 24 hours. You can also apply antibiotic cream two to three times a day, although this isn't absolutely necessary.