@burcidi-- I don't think so. Three weeks is too long as an incubation period for a common cold. The incubation period is usually a few days in most people, but it can be up to a week. If you had said two weeks, then I would have said maybe, but I doubt that you picked up the cold from your friend.ymptoms can appear in just a few hours or as long as 10 days after exposure. The average incubation period is one to three days. Medications do not affect the incubation of a cold, nor do they eradicate it unless it is accompanied by a bacterial infection.