Well, in my opinion, I do not think eye stye can transmit to your kid from you. So you do not need to worry about it. Generally speaking, you should know that a stye is inflammation of the eyelid, usually inside one of the small glands lining this eyelid. And for the causes, most styes are caused by infection from bacteria. But on the other hand, there is no evidence which have shown that it can be hereditary. So your kid will be fine. But for your situation, you should try some ways to cure it. For example, the tea bag contains many different objects which do a good job to many eye diseases including stye. In my opinion, you can just try tea bag. Anyway, just pay more attention to it.