Hi A.,
Viruses do hang on a lot longer in kids (especially infants) than in adults. Three or four weeks is totally normal, based on my son's experience and what his pediatrician said. Coughing more in the moring is often from post-nasal drip during the night that collects a bit in the bronchial tubes. I'm always that way when I have a cold. Try running a hot shower to steam up a small bathroom and hold your daughter in the steamy room for 15 minutes before bedtime to clear some of the congestion. Also run a cool-mist vaporizer when she is sleeping. Don't add anything, like menthol products such as Vicks, at this age. Email me if you want more on why, but suffice it to say that the pharmacist we spoke to back when our son was about 18mos told us pretty scary stuff about using menthol in kids younger than 6 years-old. What method are you using for taking her temp? At that age, were told that using a digital one under the armpit was safest and that anything over 99 degrees (using that method)was potentially a fever. Many of the forehead strips and at-home ear thermometers, etc., are not terribly accurate, but neither is the armpit method. It's just apparently the best, non-rectal way to take a reading at that young an age. Taking the temp rectally (booty) is the most accurate. If you get an armpit reading over 99 degrees, the rec is to follow it up with a rectal reading (with a thermometer approved for taking temps rectally). Also, consider the timing of when you take her temp. Try to take it after a period of calm. Also, one's temp tends to be lowest first thing in the morning before getting up, which could be misleading. Here is a link to Lucile Packard Children's Hospital at Stanford re: taking a child's temp: http://www.lpch.org/HealthLibrary/ParentCareTopics/FeverI...
Anyway, my only concern would be that she might have an ear infection, though if her fever has been trending down (on its own, not because of Tylenol, Motrin, etc.), she probably doesn't have, or no longer has, one. Btw, many docs no longer advocate treating ear infections with antibiotics, etc., anyway and just let mild ones run their course. I do recall that coughs and sniffles seemed to persist forever until my son was about 4 years-old. The fact that she is acting happy is a really great sign. If she had something more serious, you would likely notice changes in her behavior and eating. I hope her cough and sniffles go away quickly!