Some types of sinus infections are contagious and some other types of sinus infections are not contagious.
If your sinus infection is caused by a virus then you are contagious with your sinus infection.
But if your sinus infection is caused by bacteria then your sinus infection is not contagious.
When you have a bacterial sinus infection the bacteria sinus infection cannot spread to other people and infect them and with a bacterial sinus infection antibiotics can help.
If you have virus sinus infection then antibiotics cannot treat the sinus infection caused by a virus and you'll be contagious with it.
If it's the virus sinus infection you should stay off work or out of school until the sinus infection clears up.