Pls no worries. It is a common problem. There are many possible reasons causing it. At first, When you are singing, you are just stretching the muscles in your face, and then your tears will spill out. Apart from this fact, the reason to the problem is that you make the voice focused to your nasal cavity, and then the vibrations would make your face tingle. Of course, because this situation do not mean that there is disorder of your eyes, so if you want to solve this problem, you can just make your sound lower and then the voice will come out from your stomach. Meanwhile, maybe you are a little nervous while singing, if so, you can just relax yourself and have you at a ease.
Tears of the people are all the time to produce, however, it is very little, so you will not feel the tears flowing. In fact, not only yawning, laughing, sneezing, coughing, vomiting, shouting and so on, also can led to tears. Most are also the same reason, these actions are accompanied by a very large mouth open and a lot of air exhaling from the body to exhale carbon dioxide and inhaling oxygen. After a series of reactions, the tears cannot go on, more and more are produced in the eyes. Go on like this, you will be tearful, and finally you suffer the tears and cannot stop.
Maybe you are so emotional and the song is so moving which causes you to tear. However, about the aspect of health, you may have the rhinitis. Once you sing, there is the nasal vibration which may indirectly cause the increase of tear excretion. That is maybe the main reason why your eye come out tears when singing.