Can a gnat fly up your nose and lay eggs in your sinuses?

They are certainly small enough to do this, but they prefer to lay their eggs on the soil of house plants. So the answer to your question is "possible, but not likely".

http://pestcontrolcanada.com/INSECTS/Flies/Gnats.htm

If you're a sheep. Or a deer. (Or probably any of the ruminants. Just guessing.)

Well, sorta.

"Flies deposit as many as 500 larvae in the nostrils of sheep. The larvae then move up the nasal passages to the nasal and frontal sinuses."

Those are bot flies.
http://ipm.ncsu.edu/AG369/notes/sheep_bot_flies.html
http://www.britannica.com/EBchecked/topic/155571/deer-nose-bot-fly

I have personal experience with the human bot fly, but the larva just got under my skin, not up my nose!
http://ambergriscaye.com/pages/town/botfly.html

I've heard the bird of paradise can fly up your nose...

Using St Anselm's Proslogion (for Gnats, rather than God):

1. One can imagine a gnat flying up one's nose and laying eggs.

2. We know that gnats in reality are greater than gnats in the mind alone.

3. If a gnat able to fly up our nose and lay eggs we imagine exists only in our mind, then it is not a "gnat which none greater can be conceived", ie. a gnat that you're darn tootin' can fly up our nose and lay eggs.

4. A gnat which none greater can be conceived must also exist in reality.

5. Failure to fly up our nose in reality would be failure to being a gnat which none greater can be conceived.

6. Thus a gnat which none greater can be conceived must exist, and we call this being A Bloody Nuisance.

https://en.wikipedia.org/wiki/Proslogion

And I thought Annoy the Editor Day was June 8th?

Or maybe this is Annoy the Wikipedia Editor Day.

:D

I told him to just take the whole month to celebrate...and get it out of his system.

Surely the gnat should be lesser rather than greater? A very great gnat would not be able to fly up one's nose - unless the nose in question was the greatest nose conceivable... But what if the gnat has sufficient velocity to fly past the sinuses and intrude into the cranium? Surely it would then be both in reality and in the mind?

Whoops! June 10th.
(Must have a gnat up my nose.)

Actually the 1st Annual Annoy the Editor Day was June 8th, but it is very fitting that it is actually celebrated in subsequent days and perhaps in months, much like how the Grammys are structured.