Could an increase in cold sores be a sign that I'm coming down with novel coronavirus?

Nonspecifi. This could be a non-specific sign that your body is being stressed. Cold sores could appear.
Immune system stress. Cold sores are caused by a herpes virus (HSV-1), not a coronavirus, however it is believed that outbreaks occur when our immune system is stressed. This can be due to a variety of factors: lack of sleep, poor nutrition, emotional stress, other infections. It is non specific, and not specific to any particular disease. It "could" be due to your body fighting another virus, or it could be stress.