Burn question

I was grilling the other day and reached over to one side and singed my arm on the lid just a little. It burned at the time, but I ran it under cool water and dried it and went on with my night (it was a little sensitive, but nothing that was going to keep me awake at night). It eventually blistered like a welt (looks like a 1" scratch on my arm), not to big though. I guess at some point the blister ruptured and the skin dried where it had popped, it dried out and the skin really started to irritate me. So, of course, I pulled off the piece of skin that was stuck there because it felt like a needle in my arm.

Now it's drying out more and I want to prevent the skin from getting dried like it did after the rupture. Is there anything I can put on it to keep the skin sort of pliable or something? Or do I just wait for it to scab over? It's been a while since I have had a burn like this. I just don't want it getting infected.

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