All cold sores are contagious so you should avoid kissing someone or making contact with anyone while you have the cold sore until it's gone.
Cord sores are caused by the virus called the Herpes Simplex Virus and it's very contagious to other people.
You can kill the virus on the cold sore and get rid of the cold sore by applying some apple cider vinegar to the cold sore 3 times per day with a cotton swab and since Apple Cider Vinegar is antiviral and antibacterial it will naturally kill the virus causing the cold sore.