When to take a newborn to the doctor?

Lillian • 19 years old ~ Married ~FTM to identical twin boys ~

My baby is 2 months old and has been coughing every few minutes, has a stuffed up nose, and has a few times coughed to the point of spitting up his formula while feeding. He is constantly fussy and needs to be held all the time or he cries. And he usually doesn't cry. So how do I know if I need to take him to the doctor?