If you don't treat the cold sore it can take a week or 10 days for the cold sore to go away and heal up on it's own.
You can get rid of a cold sore faster by applying some baby Orajel to the cold sore which will help to numb the cold sore and and help it go away overnight.
Whenever I have cold sores I use baby Orajel on the cold sore and it helps to heal the cold sore overnight for me.