Girls, hello! My son has a runny nose that hasn't gone away for a week…

Girls, hello! My son has a runny nose that hasn't gone away for a week. I'm treating it with Aquamaris and doing inhalation with a physical solution. He still has mucus. There is no cough, the pediatrician said if there was a cough, we should give antibiotics. I think maybe we should give antibiotics now so the runny nose goes away? He's two months old.