One can get pink eye in both eyes at the same time, but it usually starts in one eye first, then progresses to the second eye.
In fact it's typical for only one eye to be infected.Since conjunctivitis may begin in one eye but often spreads to involve both eyes, so if you have one pink eye, you should wash your hands often, wear glasses, and never touch your eyes to prevent worse infection or your other eye from getting infected.
If you get one pink eye, you'd better accept the treatment as soon as possible. Or else, the other eye may get infected quickly. You should pay attention to your use of eyes by keeping the good habit of hygiene. Then, you should keep using eyedrops to release the symptom. You should keep in mind that not eating spicy food, drinking and smoking.
Yes, pink eyes can appear definitely at the same time, but it usually starts in one eye, and the pink eye is contagious, thus the other eye can be infected later. Both eyes with redness and itching start at the same time are often because of eye allergies. Hence, you should avoid using your hands to touch your pink eye to prevent the other one get pink as well.