I wouldn't say it's not normal. if you're on medicine, I would just keep taking it, make sure you're eating healthy and drinking lots of fluids, lots of rest, the usual "get better" stuff. if you aren't getting better within the next couple of days, set up an appointment with your doctor (if you haven't already) so you can get a good treatment. better safe than sorry!
If you're sick for this length of time, you should probably consider seeing a doctor to find out what is wrong with you, and what you can do about it. OR You could have a little cold, but you're up too late on FunAdvice when you should be sleeping ;) The best medicine is rest. Try to get some sleep, see if it goes away, if not, consult a doctor.
If it's just a flu and it is slowly drifting off, then yes its normal, its just taking its time. But if you have had fevers,and your body hurts, and coughing non stop, and all that stuff that you get on the first days you get sick, best thing to do is to go see a doctor, it could be something more than a cold.
Yes,if it is the flue .Be sure to drink plenty of fliuds and eat food .If your cold dosent pass you may want to see a doctor .