Is it normal for babies to have yellow discharge in there eyes almost to the point of being sealed shut?

Common, and depends: Babies often have blocked tearducts and usually wake up with gooey material on/in the eyes, more so in the areas close to the nose corners etc...As long as the eyes themselves are not red, baby should be ok..Gentle wiping with warm towel and massage on edges of nose will do the job. It may last 6-12 months. But if the eyes are red, possible pinkeye and needs to see a doc.. Good luck and congrats.

Nope: Sounds like viral conjunctivitis. Other possibility is blockage of tear ducts-have it checked out by ophthalmologist.