Most sinus infections go away on their own without the need for antibiotics.
Also some types of sinus infections are caused by viruses which means that the antibiotics cannot do anything for them.
If you're infected with a bacterial sinus infection then taking antibiotics can help and would be a good thing to help the sinus infection go away.
But with a virus the only thing you can do is really wait it out and eventually within a week or two weeks the sinus infection should go away.
If not then see a doctor.
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.