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Is this a cold sore?

So my lips have been really chapped recently especially on my bottom lip and I've been picking it off cos it's annoying me and now I've kind of got a scab that I've still been picking as it's also chapped and is annoying me. Is it a cold sore? I've never really gotten any before and no I've not kissed anyone and no one I live with has a cold sore we're not the type of family to kiss either so I've not caught it off anyone.

According to the NHS website a cold sore starts off with itching/tingling/burning but I never felt any of that just felt like dry/chapped lips. I feel like it must have bled/got damaged while I was picking at it and then it scabbed or it's a cold sore idk