It has not undergone clinical trials for this so no one can tell if it has the ability to work. Some preliminary research in animals suggests that CBD (and THC) may actually hinder the immune system's response to certain infections.
I think there is a lot of hype about CBD oil without a lot to really back it up. If I had a cold and fever, I'd take ibuprofen. But remember, a fever is our body's natural defense system working. It's usually not dangerous. Our doctor says to make yourself comfortable such as a light blanket if you are chilled and cotton pj's in case the fever breaks and you get the sweats. And simple comfort meds like ibuprofen or Tylenol if you feel it is necessary. But CBD oil would certainly not really be the first thing I'd go to.
If you have a cold and flu, you can use over-the-counter medications to relieve symptoms of the cold, including runny nose, sore throat, cough and congestion. Over-the-counter medications are usually quick and effective.