Most Sinus Infections only last a couple of weeks even without taking any antibiotics and if the sinus infection lasts longer than 2 weeks then you might have a more serious type of sinus infection and should see a doctor about it.
If you take antibiotics the sinus infection could go away within a week or sometimes sooner.
When I had a sinus infection and took antibiotics for the sinus infection it went away within 1 week although I was starting to feel a bit better within 48 hours of taking the antibiotics.
It's best to stay home for at least 48 hours after taking antibiotics for the sinus infection so that you'll feel better.