Yes. There are no universal herpes symptoms; in fact, some people with herpes show no symptoms at all. There is also a variation among people who do show herpes symptoms. So, not everyone will have the same symptoms.
The first classic symptom of a cold sore is a burning or tingling sensation around the lips or nose. Within a day or two there is an eruption, which can lead to visible fluid-filled blisters. These blisters break exposing an open sore. If left uncovered, the cold sore will dry out over a period of days. A scab will form and then fall off once it’s healed.