Griffe, for your skin burns, you can try two things to help ease them and heal them a bit: aloe, and oatmeal soaks. Aloe is a plant that is wonderful for any type of burn. If you or a neighbor has a plant, cut a stalk and then cut it open to the gooey stuff, and smear it on your burns.
Using oatmeal will also ease a burn. Put any type of oatmeal, uncooked, into an old sock, or rubber band it into a cloth, any way it won't actually get into the water directly (or it makes a clean up mess.) Then put it into the water you have to soak your arm etc... water should become milky looking. That means the oatmeal is breaking down and working. It works great for any type of itching also.
Usually if a burn is open and oozing though, you shouldn't put anything on it and seek help immediately. (They just have to clean off what you put on, such an bandages etc and that might open it up further.)
Go and tell them you must have blacked out and can't remember how it happened. If you don't know, you don't know. But do go get help, you don't want to lose your arm to gangrene infection!