You may get pink eye without redness in the beginning of the disease. But later the redness will show up if you got pink eye. Burning and itching can be a starting sign of pink eye, but it can be caused by other reasons too. You can apply some artificial tears to lubricate your eyes. If the symptom persists, I suggest you to put a piece of ice on your closed eyes to calm down your irritated eyes.
I think it is impossible to have pink eye without redness. Pink eye often have the symptoms such as redness in the whites of the eyes. Itching and burning eyelids, swollen eyes and a lot of tears. Among these symptoms the redness appearance may be the most apparent and common symptoms of pink eye. And this is why we call this kind of eye problem as pink eye. But when the viral or bacterial is in its incubation period, we may not notice all the symptoms immediately and directly. That's why we need to see an eye doctor for some professional exams and treatment. Hope this helped!