Newborn help

Okay so my baby is 3 weeks & he hasn’t had an weird symptoms but just now he spit pretty bad & lots of snot came out of his nose. It kind of scared me because through all this he started turning red & then calmed down.. this may sound silly, but I didn’t even think newborns that young could rid their own snot. Anyway, I just wanted to know if something like this is normal or if I should get him checked out?

Also after the incident I googled some stuff & it suggested that you should periodically suction your babies mouth, along with the nose to get rid of build up & I wanted to know if any of you do their mouth as well