When you have green mucus it usually means you have a viral infection and not a bacterial infection.
Since the infection you have is a viral infection then the antibiotics will do nothing to help with your viral infection since you have green mucus.
When you have a bacterial infection then the antibiotics will help but not when you have green mucus.
However sometimes green mucus can be a bacterial infection so if your infection doesn't clear up and you have yellow or green mucus then you might want to see a doctor to find out if it is indeed a bacterial infection and if so then sometimes the antibiotics might help.
But usually waiting out the bacterial or viral infection is enough to cure the infection but sometimes antibiotics can help.