Probably not. Cold sores--or herpes simplex reactivation--usually will present as an area at the lip red border or just beyond, that initially may sting or burn and then goes on to develop a cluster of tiny blisters. These may coalesce into one or more larger blisters and finally open. Cracking at the corners of the mouth is often from licking due to dryness (ie allergies).
Fungal infection. Cracking and chapping in the corners of the mouth is usually not cold sores, but is a condition called angular cheilitis, due to a fungal (yeast) infection called candida. It's common in denture wearers and others where the bite is over closed and where drooling tends to occur. An antifungal cream, nystatin, is used and the denture may be soaked in Nystatin solution. A new denture may be needed.