My cousin had a pretty severe allergy to dogs as an infant/child. Her parents were in denial for the longest time...it wasn't until she was about 2 that they got rid of their dogs. For those 2 yrs she had a brutal smokers cough. Once the dogs were gone, so was the cough. Some allergies do result in a cough...but I would suspect this is in fact a cold. If it is allergies it won't magically disappear, it would last a lot longer than a typical cold! That would be the true telltale sign I think.