I have no such experience. I don't think it is ok. You'd better go to the hospital to have a check on the eyes to see whether the eyes get the infection. It is the infection that causes the eyes get watery. You could use some eye drops now to get rid of the bacterium in the eyes.
So, it looks like you are curious about that phenomenon. Anyway, sometimes I would encounter that situation when my nose hair was unintentionally pulled out. So, it is quite normal to make your eyes water. Because there are many nerves in our nose connecting our eyes and nose,which could give rise to some hurt feelings, and lead to watery eyes. I recommend that you try to use some shaver to help you, rather than pulling out your nose hair.