I believe that your eyes are constantly exposed to those glow sticks. Anyway, as far as I know, those sticks could be frequently seen on some special occasions
suich as a concert or party. They are of course harmful to your eyes if you keep looking at them because they are the only light source in the dark environment, which makes your eyes tired and exhausted, leading to an eye strain or some other problems.
Frankly speaking, I am not sure what kind of effect seeing glow sticks will bring to eyes. It seems that there is no such report. The chemicals in glowing sticks are three components, hyperoxide, ester compounds and fluorescent color. The working theory of glowing sticks is the chemical reaction between hyperoxide and ester compounds can release power which makes the fluorescent color glow. This light is not very bright so technically it is safe. It is commonly used devices in concerts, balls and various parties. It is popular used for decoration, toys, rescuing in sea, military lighting and signal in night and so on. As long as you don't split the chemicals on your skin and into your eyes, it should be OK to see the glowing sticks. Don't worry.