Vicks can help alleviate the runny nose symptoms but Vicks cannot cure or stop a runny nose.
You can take Nyquil Severe medicine which can help to dry up the nasal passages and stop the runny nose.
You can also use a saline solution and use a Neti Pot or something else to rinse your nasal passages out to clear up the runny nose.
Staying hydrated and using a humidifier or taking a steamy shower can help clear up a runny nose.