He might have some fur or somehting backed up in his nose. I would sure go
to the vet. The rubbing the nose is what makes me worry. If something is
stuck there it might turn into an infcection.

If there's no discharge, I wouldn't be too concerned.  It could be dust or
something that's bothering him.  Could be the new cat litter.  Of course, if
it keeps up and there's a change in behavior, contact your vet.

Denise,

Our cat Fred has also started frequent sneezing now for 2 days.  He just went
to the vet 4 days ago for a routine checkup, and it was very stressing for
the poor guy, and now he's sneezing and licking his nose all the time.  He's
also kind of sluggish.  We believe it was due to the stress lowering his
immune system, and him being around the germs or other cats in the vet office.
Vet offices aren't as sterile with germs as human hospitals, as I worked at
one as an assistant and know first hand that the vets and assistants don't
wash their hands too frequently.  Humans don't seem to catch colds from dogs
and cats, so they don't realize all the germs floating around there.  We also
have a second cat.  Hopefully our second cats won't catch the cold.  I'm sure
they will be Ok, as I believe it's no more serious than us catching a cold
generally.  Just look for a yellowish discharge or other symptoms.  Hope your
kitty feels better!

Wendy