vomiting is usually associated with what is called the "stomach flu," which isn't related to influenza in any way. This is a total misnomer.
As far as the differential diagnosis of influenza vs. a cold....I think e_dawg's response is the method most commonly used. I know there are influenza antigen tests (ELISA), and at least experimentally there are PCR-based tests. Colds rarely produce a fever, at least not a significant fever. Influenza does. Sneezing, stuffiness, and a sore throat are more common in colds than influenza.
You can have symptoms for two weeks or more. One gets symptomatic with influenza 1-4 days after contact with the virus, some people are contageous for over a week. And typically a strain will be circulating in the population for the entire flu season (November-April, looking back over infuenza prevalence charts).
Just an FYI - the CDC has some great info on influenza, and many other diseases. Check out
www.cdc.gov and hit the "Diseases A to Z" for some good information. What I like about the CDC is that they have info for the common person and for the health care professional, often allowing somebody who's really interested to dig deeper and to learn what the pros are told (epidemiology-wise at least)