Sinus infection is what they told me Otis had too. A month of antibiotics and his nose is still gross. It's not all the time, and only one side of his nose.. but its still runny, green and nasty. He has been on antibiotics for the Lyme's disease and antibiotics for the sinus infection twice a day, every day for over a month. If there was any kind of infection anywhere in his body I'm quite sure it would be dead by now. I'm pds his body is a completely sterile environment by now.
So... I just carry tissues all the time and wrestle him to the ground to wipe his boogers.
I hope you have better luck with the antibiotics and his problem clears up for you.