@BAADATTITUDE ,
For starters, Neosporin is an antibiotic. Not a bad idea, but it only promotes healing in the sense that it reduces the chance of infection. At one time, it was popular to oil the area with Vitamin E. We'd get a bottle of those little gel caps, pierce them with a pin and spread the oil over the wound. If it didn't work, we always thought it would.
Peroxide is another treatment that treats infection but does not otherwise do anything to speed healing. Like rubbing alcohol, I'm pretty sure can do more tissue damage than not, if you overdo it.
Did your doctor understand that you were treating a friction 'burn' and not one caused by heat? They might be different. What did she suggest when she told you this.