what type of burn is that I have, and should I go to the Doctor?

I burned myself with a curling iron, and had once before but never this bad. It wasonly on my arm for few seconds, the temp on the curling iron was set for over 300degrees. At first it did not look to bad Black and red in color then it started to blister in one area of it...A few hours later it started oozing and now it is bleeding in the center area...And still black/dark in color all the way around the area that is oozing and bleeding. I have been placing antibiotic cream on it and keeping it wrapped. It does ooze through the wrap. Its about 3inches long. Will this heal on its own ? Or should I go have someone look at it?
I should have mentioned that the blistered area did pop, and on is own. That is the area that is oozing -not pus like, its clear and then parts of it is bleeding as well.
Thank You Everyone for giving me some advice !
 
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