"Cold sores" have nothing to do with colds. They're caused by the herpes virus. Assuming that you don't have herpes, what you've probably got is a canker sore, which looks similar but has different...
Yes. A cold sore is a type of virus and it doesn't matter if you have a cold or not. The cold will not cause the cold sore but your immune system might be weaker making you more susceptible to it.
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