Thanks for the query,
It is not cold sore
Cold sore presents as water filled lesions
Also cold sores are itchy.
A photograph would have helped me better.
Apply some moisturising lotion
Also take an antihistamine tablet.
This will give you some relief.
Please meet a dermatologist
for exact diagnosis.
Let me know if you have any other doubt.
you can ask a direct question to me on this forum, following the below link.
Wishing you a good health.