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It might be a cold sore
but it is more likely eczema e.g. contact dermatitis
Whatever it is you should stop applying any irritant like after shave, soap, dettol, savlon.
You need to apply Vaseline or petroleum jelly twice or thrice daily.
You could apply a combination of Fusidic acid
1% cream / ointment twice daily for 1 week
You should consult us 1 week latter.