Cold sores do eventually go away on their own even without treatment within 2 weeks at most.
The cold sores that people get are caused by the herpes simplex virus and is not an STD.
The cold sores are mostly an annoyance and not anything serious.
You can apply some toothpaste to the cold sore or a cool compress to the cold sore and it will help it heal but either way the cold sore should heal within 1 to 2 weeks.
I've also applied some apple cider vinegar to my cold sores and usually the cold sore goes away within 5 days when I apply some apple cider vinegar daily.
Cold sores cannot go away overnight and nothing you do will help a cold sore heal overnight but you can usually help the cold sore go away sooner than it would if you hadn't tried any home remedies for the cold sore.