My three week old is coughing 😭

Everyone in my household got sick. We all got the flu shot btw. We tried our best to keep the baby away but then I got sick and was told not to stop breastfeeding. He’s starting to cough now every ten minutes or so. What do I do?! I remember with my first he was three months when he got sick for the first time and he got a high fever and was such a horrible situation. I can’t take him to the doctor yet because he’s not showing any other symptoms, can I?