Sometimes in first aid emergencies, you must work with less than optimum materials. Especially if significant bleeding is involved, don't worry overly much about sterility. Th victim will perish within minutes if bleeding is not stopped. The hospital can deal with infection, if necessary, later on..

I believe you are correct for bandage sterility, but milk is pasteurized at around 175F for ten minutes or so -depends on the product. I don't thin hot ironing will induce sterility, especially in a back pocket (if it is anything like mine...)