When you have a sinus infection caused by bacteria and you're prescribed antibiotics for the sinus infection the antibiotics should begin working on the sinus infection with a day or two.
Then after 4 days of taking the antibiotics you should start feeling much better.
Most Sinus Infections go away on their own within a week if the sinus infection is not caused by bacteria but you can go to a doctor just to find out what kind of sinus infection you have.
If it's a bacterial sinus infection the doctor can prescribe you some antibiotics to help you recover much sooner.
If the sinus infection is not bacterial then the doctor may prescribe you some other medication and just send you home and have you rest and stay hydrated.