Is it possible for your cold sore to travel from your top to your bottom?

My cold sore started at the top lip and now is pretty much healed it's been 5-6 days. And all there is is a little itchyness still but I looked at my lip this morning and I have a bunch of little bumps all the way across my bottom lip. The same as what my top was 5 days ago.
Is it possible for your cold sore to travel from your top to your bottom?
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