My 2 year old daughter has a mild cold. she keeps getting gunk coming out of her eyes. what is this and is it contagious?

Maybe: Sometimes the virus can also infect the eyes, in which case it is contagious. Usually the eyes are red and swollen. More likely, the virus is causing some dryness and irritation, which can lead to white 'mucoid' discharge.

Conjunctivitis : She probably has conjunctivitis as part of an upper respiratory infection (cold). It's most likely viral, in which case antibiotic drops won't help and it may be contagious. Another possibility is nasal congestion from the cold causing blocked tear drainage ducts. A nasal decongestant might help if this is the problem, and it's probably not contagious. See your pediatrician or ophthalmologist.

Infection: It is very common for a cold to 'settle' in the eyes. It is most likely a virus that will take several days to a week to resolve. Her body's immune system will take care of the infection. If the discharge increases she may need eye drops.