So, I think there must be something wrong with your eyes. Because we simply don't get burning and watery eyes without an infection, which means that your eyes are probably infected with something. From what I know, burning eyes are watery eyes are interconnected, both of which are symptoms of infections, so it is quite normal for you to experience that. Hope you get immediate medical treatment and take care of your eyes.
It is really strange for you to have burning eyes when you get watery. You may get infection at the eyes because of the invisible bacterium. You should take great notice of it. You could use the eye drops with anti-inflammation to get rid of the bacterium. You could also use the warm compress to make your eyes feel comfortable.