I had a similar event, but in the end, I didn’t have a nasty scar. I have a thin white line where I was burned. You can use tribiotic ointment to keep it from getting infected. You can use Aloe gel or lavender essential oil to help healing. If you are worried about accidentally bumping or scratching it you could put a bandage over it.

Liquid bandage works nicely on skin regrowth.
If the burn is deep enough, you will get skin buds. If that happens, don’t be alarmed. However, skin buds itch like nothing else.

I had skin buds with a laceration once. They are temporary and kind of cool. They speed healing.
They look like a bumpy rash, but the appearance will be covered by smooth new skin.

If you think you might need a doctor to look at it don’t hesitate to go and see one.

First what NOT to do. You already found this out the hard way, don’t use creams, lotions, butter, antything with cortisone, or dressing that the fibers can get caught in the wound. Don’t break blisters. Resist scratching.

You have to be careful it doesn’t get infected, but you are probably past the point of that being a very big concern. Still, if it becomes more inflamed, more painful, developes pus, or if you get red streaks traveling from the wound up your arm, you must go to a doctor. The red streaks are an emergency!

Do use a thin layer of Vaseline or antibiotic ointment. Note: do a test spot on regular skin to test for allergy. Best if you have used the ointment before with no problem. Still do a little test on the other hand. Clean the wound once a day gently with soap and water and replace the dressing. Use liquid soap that has no fragrance and you know you are not allergic to it.

If the pain is bad Tylenol is good for this type of pain.

Lastly, I don’t know what you did immediately when you burned yourself, but just trust me on this, when you burn yourself, immediately put that area in cold water. Your hand should have gone immediately to the cold tap water and just let it run over your hand for a minute. It does significantly reduce the burn. Even a burn from touching hot metal as you did. This goes for little burns also, and when you burn your mouth on food. For food take cold water into your mouth, hold it for a few seconds and repeat three or four times.

Cold running water, or even if it’s not running, right away is not to take the sting away, which it does help with, it’s to literally prevent the burn. Ice directly on the wound can harm the skin, but it’s ok if there is some ice in your water, don’t get too worried about the perfect temperature of cold. The trick is immediately after. Do it no matter how minor you think the burn is, just always do it. Just try it once if you never have. Humor me.

When my son was younger, he got a bad burn from a law mower. The doctor debrided it – taking the scab off – and told him to do it every day I don’t think your scab coming off is a bad thing then but I’m not sure if it should be covered or uncovered. Maybe you could just call your doctor’s office.

I keep a bottle of 100% pure Aloe Gel on my counter for those times that I get burned. The aloe gel seems to dry out the blistering faster than using nothing & it appears to me that the burned area heals faster & with less scaring.

In your case, I think I would continue applying the Vitamin E Oil & just STOP covering with the band-aid. Fresh air helps to heal a sore faster & the Vite E helps to diminish scaring. IF you catch yourself scratching at night, just use a band-aid at night before going to bed & remove it the first thing the next morning. I only use band-aids for the initial protection in .the first few days so the wound doesn’t get infected. After that I use a disinfecting ointment until it heals further & then the Vite E oil to decrease the chasnces of scaring.

I’d just keep it clean and leave it alone. It’ll heal.

Keep it clean and apply a triple antibiotic ointment like Neosporin to keep it from drying out. A clean bandage every day or every couple of days won’t hurt.

I’m going to contradict @janbb because that sounds like something that was done in the past, but now would not be thought of as a good treatment. There were old wet to dry dressings where the wound/burn was cleaned out 2–3 times a day, which was a similar idea, and also I think was tossed out as much less than ideal treatment. This is not to be confused by what medical professionals do for severe burns in hospital, which is a whole different thing. Don’t take my word for it though, I’m not an expert, although my sister is, but I haven’t had a chance to ask her. Ask your doctor, or at minimum so some googling for current burn care methods.

If you have scabs, and are worried about a bad scar, you could pull it to start with the ointment treatment, but it will open you to infection again, and if it’s already been several days probably some of the scarring is already starting and you can’t really start from scratch. You might wind up with very little scarring though anyway, Especially, if you are very white/pale.

The ointment will keep a scalp from forming quickly to begin with.

I would use Manuka honey on it, fabulous stuff, it has been my go-to remedy for wounds and burns for 25 years. Use generously, put the honey on the dressing, not directly on the burn, and change dressing every day or two, more often if it is exuding anything.