Yes Tea Tree oil can get rid of cold sores when you apply the tea tree oil to the cold sore.
But first before applying the tea tree oil to the cold sore you need to dilute the tea tree oil in some carrier oil such as coconut oil or Jojoba oil to avoid the tea tree oil harming your skin.
After diluting the tea tree oil in the carrier oil take a cotton swab and apply some of the tea tree oil to the cold sore and leave it on the cold sore overnight.
You can also apply the tea tree oil 2 to 3 times per day everyday until the cold sore goes away.
Applying the tea tree oil you should see the cold sore disappear within a few days.