Chances are it has an upper respiratory infection aka URI.  The common cold
for the cat.  If the cat is eating and acting fine, then there isn't much to
worry about, but if its starting to not eat, or is lethargic, you should get
it to the vets for some medical help  to help him get over it. :)

Yes, cats can get colds and can have allergies.  Like humans, if it is a
virus, it has to run it's course.  How can you tell?  I don't think you can.
Make sure he continues to eat/drink and otherwise act normal.  If he stops
eating get him to the vet.  Another thing that might help, stick him in a
small room w/a vaporizer (yes like they used to do w/children), a few times
a day.  It does seem to help them breath a bit better.  I have one
w/re-ocurring stuffies and it does seem to help him after a few
"treatments".
You can use plain water or you can use the oil stuff as well.

Yup, had a cat that was alergic to dust which meant moving beds and
vacuuming under them monthly or he would be in fits.