Kissing can cause red eyes. There are two situations you need to pay attention to. The first situation is that you would be nerve and excited when kissing which will make your blood pressure higher. In this way, the blood will flow to the eyes and then make the high eye pressure, thus will make the red eyes. The second situation is that the person you kissing got red eyes, because red eyes can be infected, it is possible for you to get the red eyes.
Actually the kissing behavior will not cause the red eyes. Even if you feel shy, it is the face that will get red. There may be one reason to explain this. Your partner may get the pink eyes which will be contagious to you. You should check you both eyes and see whether you guys get the pink eyes. If so, you should treat it carefully.
Yes, it could cause that. Pink eye is very contagious and you could quickly spread it to your lover by kissing, which is almost eye to eye contact. Because pink eye or conjunctivitis, is caused mainly by invisible and harmful objects, like bacteria or virus. It is common to see it in children, it can be seen in adults as well. Hence, it is better not direct or indirect touch others when you or your lover has pink eye.