With the burn as bad as you say, it may leave a permanent scar, which you'll have to learn to deal with, but that doesn't have to be during an interview right now. During an interview, you're likely to be self-conscious and nervous as it is, you don't need to add to it. This is about your comfort level more than it is about the interviewer's comfort level.
If it makes you uncomfortable with people staring, then cover it, but do it with a bandage, gauze, or whatever was appropriate when it was still a wound. If the dressing was bulky, you can skip it and just use an Ace bandage, so it's less visible. People might still glance at it, but it should hide the "gross" part and allow them to process the situation "normally".
This can be something you slip on right before and take off right afterwards.
It isn't to hide that you got injured, only to prevent people from overreacting. There's no shame in getting hurt in a work related accident, unless you purposely caused it, which doesn't appear to be the case.
If the interviewer asks about the bandage, you have the right to refuse to answer, but that can look bad, as if you have something to hide. A simple answer of "I was near an accident at work" should tell them enough to stave off any discriminatory questions, if they are a good interviewer. If they press for more information as it applies to your involvement in the accident, you'll know this probably isn't a good place to work as they are interested in "who's fault is it".
There are questions they can legally ask, though, such as if you are still physically and mentally able to the work they want. Things along the lines of: Since this was a burn, do you flinch or shy away from working in hot applications of any sorts; Is your manual dexterity or range of motion affected? These address your ability to do a job, but questions about how your actions did or didn't cause the accident are not likely to be relevant or legal. If you feel as if the interviewer asked the wrong type of questions, you may want to consult a labor lawyer. This doesn't mean you sue them, you just find out if those questions are legal. The lawyer will let you know if you have a case.
If you feel less comfortable with the bandage/dressing, then don't use it. As I said before, this is about your comfort level, not anyone else's. It's not your job to make everyone else comfortable with you, and if someone has a problem with it, it's their problem, not yours.
Sorry about your friend and your injury. I hope I helped and good luck with interviews!