Yes, lack of sleep will affect the blood circulation of eyes, and then lack of oxygen may lead to your eyes feel uncomfortable. Lack of blinking of eyes will also lead to dry eyes, it will also cause the burning when you wake up in the morning. This symptom may cause by excessive eyes using. The decrease of blink times will cause lack of tear hyposecretion that lead to dry eyes and visual fatigue. This time you need artificial tears to relief the dry eyes and have a good rest after that. Eyes is very important organ to your life, with 80%'s information is absorbed by your windows of your heart. Long time eye use will cause vision problems such as myopia, glaucoma, cataract etc. 
However, as for the pink eyes, this is another eyes disease. It is totally different from the red eyes that caused from lack of sleep. Pink eye is the common name of the disease infectious conjunctivitis. It is an acute infectious eye inflammation which possibly infected through articles contacts of patients, including used towels, door knobs, water faucets, swimming pool water, public toys etc. This disease would happen all the year around but especially find more in spring and summer in public places. So it usually easy to outbreaks in kindergarten, school, hospital, factory and so on. The age range of patients are from infants of several months up to eighty even ninety years’ old people. As a word, lack of sleep can not cause pink eyes.