Cold sores are not serious and they go away on their own within 1 to 2 weeks even without treatment.
The cold sore is caused by a virus called the herpes simplex virus and like all other viruses the cold sore will go away on it's own.
However do note that while for most people cold sores are not serious the cold sore can sometimes be serious for some people who have AIDS, or other diseases or a weakened immune system.
If your immune system is weakened or you have AIDS or other health issues then the cold sore virus may cause other life threatening complications if the cold sore becomes infected.
But as long as you're overall healthy then having a cold sore is really not much to worry about.
You can put some apple cider vinegar on your cold sore to help it go away or some toothpaste to help dry the cold sore out.
Other than that just waiting it out and giving it a week or two is enough to allow it to go away.