I had a cold during my 6-8.5 weeks pregnancy. I drank a lot more fluids and did natural remedies route (warm water with honey, simple saline, Neti Pot, steam showers, and one cold drug...this was done on a day that was just REALLY bad, and it helped for a bit). I normally have a cold that lasts for a week. This time, it lasted for two weeks. Mind you, there was only about 2 or 3 out of those days that it was just bad...tissues usage, unable to sleep, pain, etc.
Ask your OB for a list of safe drugs to take. You can take it to relieve the symptoms. I wished I had that list prior my first scan, it would have helped! Regardless, just take as much rest as you can, and let your body heal.
Flu has been repeated as others - you'll notice chills, body is achy, slight fever etc. I had a very mild flu once, and it was way different than a cold (runny nose, sore throat, sneezing, congestion).