Can cold sores start with a black head?

No: Herpes lablialis (cold sores) are caused by a virus that lies dormant in your body (specifically the trigeminal ganglion -which is part of the 5th cranial nerve). The virus can be reactivated by trauma, sunlight, stress, fever, etc and manifests itself as a cold sore. It does not start with or from a blackhead.

No: Cokd sores usually start at the area of you lip known as the wet dry line of your lip and move outward. Blackheads are usually more on the face in oilly areas.