Is it possible for a cold sore to spread?

Key thing is spread on your face. I know they spread to other people and know how to avoid it. My 1st ever cold sore started in the middle of my left side of my lip. Now it’s red and itchy the entire left side of my lip. I put cream on it with a q-tip every 3 hours and I don’t touch it or my face even now. But for some reason it just keeps getting wider along my lip. I have a feeling it’s going to be my entire top lip soon if I can’t figure out how to stop it from spreading across. 😫
Is it possible for a cold sore to spread?
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